I just finished watching all seven seasons of the clone wars. So maybe I can shed some light.
(warning: some fairly heavy spoilers for season 7 ahead)
The sith were in league with the Kaminoans from pretty much the start. The only jedi that was involved (up until Obi-wan met with them) was Sifo-Dyas. Sifo-Dyas ordered the production of the clone army without the permission of the Jedi council, as He had foreseen a great conflict and made plans for the republic to be prepared.
In the Legends material, Sifo-Dyas' army was funded by Hego Damask, aka Darth Plagueis, Palpatine's sith master.
Sometime after Sifo-Dyas met with the Kaminoans, Dooku intercepted.
By killing Sifo-Dyas, with him out of the way...
Dooku then hired Mandalorian Jedi Hunter, Jango Fett, to be the template of the clones. Later, he gave the plans to have all clones be given an inhibitor chip to make them execute order 66 and kill the jedi.
It's safe to assume that for the 10 years it took to grow the army, the sith were the only ones overlooking the production of the clones.
The sith also were not a force that you wanted to disobey, especially when they were the ones funding the whole thing. Furthermore, the Kaminoans didn't care who they were working for; they were more neutral, not specifically on the jedi's side (who they viewed as simply clients). There is enough evidence that the kaminoans cared more about money than about the lives of anyone.
It's also to note that in those specific episodes, only a few Kaminoans knew about the siths involvement. The few that did were the higher ups: Nala Se (the prime minister), and Nala Su (a medical technician). It wouldn't have been hard for Dooku to bribe or threaten them.