(Forgive any grammatical or name spelling errors as I type quickly)
The posts of many other explanations offer partial details which work better when considering all possibilities.It is possible that George Lucas initially intended the Kaminoans and their allegiances to remain open to interpretation or uncertain.
Addressing the scientific intentions others have mentioned for the Kaminoan intentions with clone armies, it is probable that the science and cold research was a major motive which did not necessarily mean they were loyal to any faction. Indeed, both legend and canon have reveals the following about the Kaminoan race:
1. While the differences in physical makeup and voice inflection of the Kaminoans implies manifested gender identity and/or sex traits, the Kaminoans are canonically one of the most scientifically advanced races in terms of cloning capabilities. It is known that the majority of Kaminoans were born in labs themselves, their culture having long ago adopted a practical and scientific (if morally questionable and identity compromising) approach to reproduction. Star Wars has us understand they developed their cloning capabilities in order to 'perfect'themselves. Kaminoans only began cloning armies and individuals later on after refining their techniques in order to make money. Remember, Dexter tells Obi-Wan in the diner that whether or not they are friendly depends on A- your manners and B-how big your pocket book is. In essence, this statement actually supports the information about Kaminoans and their history, (which in turn I will later show affects their motives and most likely, their lack of either determination or ability to ask questions about the people they work for, whether jedi, sith, republic, separatist, or other.
Dexter's statement is a reflection of the fact that Kaminoans advanced as a society. By all appearances, significant social class and wealth differences don't exist on Kamino. The difference in building sizes reflect function of buildings (such as on Tipoca City), and not wealth. Furthermore, Kaminoans are never seen as spacefaring aliens traveling offworld and engaging in passion, adventure, wealth accumulation, political gain, or criminal endeavors despite many aliens being found in many circles around the galaxy.
It shows us that they are content on their homeworld, and have found purpose that is independent of the goals of other factions and peoples in the universe. They are barely known of, if you remember, and Obi-Wan had a hard time finding information about the planet in the first place. If the Jedi needed to refer to archives to know about a race, it is safe to infer that they keep to themselves.
As I was building to, there is a reason for this. They created a society based on science and cold practical approaches to life. In the history of their race, they eliminated genetic weaknesses in their biology by altering the DNA of their own children, who, I've already mentioned, they had begun to clone.
Let us think about this as Star Wars fans- in a universe where many spacefaring races still struggle with the same issues as non-advanced races, such as susceptibility to greed, cruelty, sexual appetites, "death stick" and "spice" style drug use, idealism, irrationality and passion-driven impulse, the Kaminoans are never seen other than on their homeworld (or missions pertaining to their homeworld's goals).
This is likely because their society struggled in its past with the issues other aliens and humans still do. On an inhospitable world ridden with storms and raging seas MOST of the time, they had to build up a society, create infrastructure, ensure their survival, and develop scientifically on a planet that too easily could wash their cities and entire populations away. Places like Tipoca City don't just create and maintain themselves. They require engineering breakthroughs, research into natural disaster type preventative precautions, and an intense amount of maintenance.
The Kaminoans, having most likely struggled to accomplish challenging goals and balance the less rational parts of personality that can easily be upset and lead to conflict that undoes progress and prevents wisdom, probably realized that they could avoid fighting among themselves if they eliminated variables within themselves that lead to irrational and (sometimes) potentially counterproductive, if not destructive, courses of action. The instability caused by personality and sense of self, instincts to reproduce, accumulate things, money, food, etc, and instinct to fight or even kill others whose goals impede their ability to achieve their own goals...this instability threatened their race as a whole. Additionally, biological risks and plagues threaten them not just because they kill individuals, but because fear of plagues and illnesses triggers instincts of selfish and paranoid nature that often undercut order, reason, and stability. War, disease,etc... these things impeded the Kaminoans ability to be objective in surviving on such a difficult world. One person's failure to perform their duty could unhinge the whole existence. For example, if a part needed to be replaced to prevent Tipoca City from being exposed to floods or energy failure, but it didn't get done, then the whole floating city could be swept away. Yes, they are used to the water, and have a relationship with it, but losing control of a situation on such stormy seas could see entire populations drowned in an instant. All it would take for the whole city is one instrumental thing needing to be done not getting done because someone was unable or unwilling to perform their role. Maybe succumbing to an illness and dying before completing their task could leave that task undone, and not discovered until it was too late to fix.Or maybe an argument driven by passion or emotion between two individuals working on a task lasted too long, distracted them too long, for them to get the job done in the timeframe it needed to get done in to prevent disaster.
Thus, the Kaminoans expunged weakness via science, and they seem cold to us because of it. But they eliminated disease. If they couldn't eliminate disease, then they modified/eliminated the genes within themselves that made them susceptible to disease. This required cloning. But as they conquered the biological external factors that threatened them, they likely realized in time that some issues resulted from the internal factors, and would come to see those factors as internal failures. Emotional reactions and hormone driven instincts could interfere with an individuals ability to think big-picture. The big picture is crucial for the success not only of the race as a whole, but for any individual within that race. So they delved into the science of emotions, of hormones, of psychology. And as they did they realized that they were programmed with them.The only way to eliminate these issues was by changing the programming itself. Cloning became the way to do this.
The Kaminoans, over generations, evolved more and more perfected techniques to achieve the desired outcomes in grown individuals. Grown individuals who functioned rationally, impartially, scientifically, and healthily were ideal, and as such the genetics began to vary less and less, as well as the differences in personality. As the need for sex, money, higher status, wealth, etc disappeared with the elimination of the genes that instill the instincts of "self" in an individual, the Kaminoans became less and less reactive, and more and more active.
As Dexter says, the Kaminoans are friendly if you have a big pocket book, AKA a lot of money to offer. But the Kaminoans aren't living large or trying to outdo one another. You can see a practical uniformity across Tipoca City that proves it. Rather, their need for money is practical, likely providing their society and government as a whole, rather than individuals and businesses, the practical resources they need. Money funds research, money buys food, money buys safety, money buys technology, and so money funds their ability to continue to pursue their cold scientific research.
And dexter says your manners affect their friendliness to you. Why are manners important to a race unconcerned with social and cultural distractions? What Dexter really tells us in telling Obi-Wan this is that they are always observing outsiders. "Manners" doesn't mean your ability to close your mouth when you burp and cut your steak with a knife and fork into tiny pieces. "Manners" means your ability to act consistent, react rationally, respect Kaminoan wishes, and most importantly, honor arrangements already set up so that they benefitted everyone. Acting selfishly, going back on arrangements, demanding more, these are signs of instability and irrational, impulsive, and self-serving nature.
Thus, the Kaminoans having already eliminated these dangers within their own society, are not likely to just welcome unstable and dangerous behavior right back into it by inviting outsiders to their planet who could jeopardize it all. Dexter says the Kaminoans are friendly depending on how good your manners are, and as such tells us the Kaminoans value the ability to perform as one should, rather than as one wants to, above all else. Manners prove you know how you should act to achieve your long term goals with a person. Lack of manners with Kaminoans shows you lack the insight and self-control to do what is best for your own long term interactions with them, and thus, you are unstable, a danger, and not to be trusted or interacted with.
Knowing this about the Kaminoans, it is easy to understand why they ask so few questions about the origins of their employers or their purposes. While the Kaminoans know that there are secrets and separate agendas among the employers, and while they know they are keeping secrets from some jedi, it is likely that they do not realize the Jedi are not one and the same. In Kaminoan minds, logic is all that exists. Approached by Sifo Dyas, and later Tyranus, and Later Obi-Wan Kenobi, they interacted with Jedi. Dooku/Tyranus had presented himself as a Jedi to the Kaminoans, and having asked few questions of Sifo Dyas when the army was first created, the Kaminoans hardly knew the difference between sith and Jedi.They were paid to commission an army, and they did so to gain the funds they needed to continue as a scientific species operating independently of the intergalactic political spectrum. With regards to instilling a chip in the clones brains, they did so having been told it was a preventative measure for destroying rogue jedi. The Kaminoans already bred the paranoia and irrational sides of their personalities out of themselves, so it is doubtful that they really retained an intense desire to know the full extent of the purpose of the chip. In their minds, just as their own culture dictated, the jedi and the republic should be acting as a whole in the best long-term interests, and if the chips are deemed necessary to the stabilization of the republic by means of preventing instability in the form of renegade jedi disrupting the republic as a whole, it is doubtful the Kaminoans really felt suspicious of this. While directed to keep it top secret, they understood their own contract warranted their own rational, unemotional, and unconcerned attitude towards the protocol. Suspicion is irrational as it is acting selfish curiosity and the self-preservation instincts of distrust without true evidence that anything isn't what they've been told, and if suspicion is unwarranted, action taken on suspicion can destabilize the business relation by instilling distrust, and creating danger, where there otherwise might not have been. The Kaminoans have survived by taking an unconcerned, detached approach to business with outsiders, and so they probably didn't put too much thought into Dooku and the Jedi chip after some slight initial consideration when they first decided to take the job and input the chip. They similarly didn't ask many questions of Obi-Wan when he came claiming to to be a Jedi. He told them Sifo Dyas had died, and they took him at face value. They similarly did not ask for proof that he was truly a Jedi affiliated with Sify Dyas, and began giving him a tour of the facility almost immediately. While Dooku and Sidious clearly intended the army to be used by the republic, and thus likely approved the Kaminoans to speak to the jedi council eventually (after all they wanted the jedi to be the face of the civil war) Dooku certainly didn't intend or authorize the Kaminoans to tell Obi-Wan so soon. It caught Dooku off guard at Geonosis, and he probably had intended to build his separatist army forces up more before revealing the army to the Jedi. But the Kaminoans revealed sensitive information to Kenobi almost immediately. As such, they likely believed that Tyranus, Sifo Dyas, and Obi-Wan were all serving the big-picture playing their parts without passion or selfish motives, and that their parts were simply meant to be independent of each other, hence the secrecy. Perhaps the Kaminoans assumed the secrecy was deliberate to prevent the "less advanced" individual outsiders from learning things that would cause them to act irrationally and jeopardized the whole objective of the Jedi and the Republic.
With regard to the Clone Wars and how fearful the Kaminoans reacted at the potential of the jedi-chip being discovered by the clone and Shaak-Ti, it is likely the fear that if the chip were discovered it would be a breach of the business contract with Tyranus and Palpatine (who they didn't know was Sidious and so likely trusted as an official representative of the republic above the level of the Jedi). The contract demanded secrecy regarding the chip, and its discovery scared the Kaminoans because it would mean they had failed to perform to their own standards, and also had failed to uphold their end of the contract which could put them at risk with their employers, but also, potentially mean that the jedi would react negatively and dangerously to its discovery, else their wouldn't have been a mandate to keep it secret in the first place. The Kaminoans thought that the chip needed to be kept secret from the Jedi because the discovery of the chip would lead the jedi to turn renegade in a way that they would not if they didn't know it existed. The emotional response they'd have to the chip's discovery would cause renegade actions by the jedi that the chips had been designed to help prevent (so they were told). The kaminoans likely considered the chips to actually simply be a preventative measure, practical, planned, but otherwise not really harmful. Unless the jedi actually ever did rebel, the chips would not be activated. But if the discovery of the chips in of itself could spark rebellion among the jedi and thus lead to the use of the chips in a way not desired, the Kaminoans feared their responsibility for failing to keep the chips secret if things went awry. That is my interpretation. Feel free to add to it.