There is only one thing that prevents the Oracle from seeing the future:
We can never see past the choices we don't understand.
The Oracle, The Matrix Reloaded
When she said that she was talking to Neo about his choice to save Trinity instead of following the normal path of The One. She knew everything that would happen up to and including Neo's decision to save Trinity, but she didn't know what would happen after that because at that time not even Neo understood why he would make that choice.
The Oracle is able to predict the future because (a) she was originally created to "investigate certain aspects of the human pysche" (as explained by The Architect) and (b) she replaced the Merovingian. The Merovingian is a trafficker of information and knows just about everything that happens in the Matrix, but the Merovingian denies the existence of choice and thus cannot see the future. The Oracle was designed to investigate the human pysche, which is capable of both rational and irrational choice, so she is able to see the future as long as each choice is understood by the chooser. Her ability to see the future is what led to the Merovingian's replacement and exile, and she took over his job trafficking all the information in the Matrix.
Since the Oracle knows everything that happens in the Matrix and can use that information to predict the future (so long as each chooser understands the choice), she can know in advance the causal chain of events which led to Neo's decision to save Trinity. The critical choices in that chain of events are easily understood:
- Persephone's decision to betray the Merovingian is obvious since the Merovingian cheated on her (almost certainly not for the first time). Persephone is clearly unhappy with the Merovingian because he has changed since they first came to the Matrix (as we find out when she demands a kiss from Neo and bitterly advises Trinity that "[love] is not meant to last"). Persephone's unhappiness is heightened by the fact that she is evidently a program designed to study love (since she demands a kiss from Neo in The Matrix Reloaded, and Ghost and Niobe in Enter the Matrix, in order to study Neo and Ghost's love for Trinity and Niobe's love for Morpheus). The Oracle would know all about the Merovingian's cheating and Persephone's unhappiness so she just had to send Neo to the Merovingian at a time when Persephone would be upset with the Merovingian for cheating yet again. The Merovingian's dinner at Le Vrai in which he was going to serve the orgasmic cake to the attractive woman was the perfect time -- hence why she told Neo to
Be there, at that exact time, and you will have a chance.
- Based on the timing requirements for The One to reach the Source (as explained by the Keymaker), Neo was going to need help from other hovership crews (one of which turned out to be the crew of the Vigilant). It's easy to understand why Soren, the captain of the Vigilant would choose to help Morpheus and Neo since Soren had been the first to volunteer to look for Morpheus' hovership the Nebuchadnezzar.
It's also easy to predict the fact that the Vigilant would be destroyed by Sentinels. The Sentinel army had already started digging toward Zion, and the hovership captains at the Crisis Meeting had already indicated the increasing risk of detection by Sentinels when broadcasting into the Matrix:
Morpheus: My apologies to all. As you are undoubtedly aware, it has become increasingly difficult to locate a secure broadcast position.
Vector: Squiddies got all our best spots.
Ice: Mainlines are crawling with them.
Ghost: And if Niobe's right, in 72 hours there's gonna be a quarter of a million more.
Ballard: What are we gonna do about it?
Niobe: We're gonna do what Commander Lock ordered us to do. We'll evacuate broadcast level and return to Zion.
The Matrix Reloaded
All of these major decisions involve a choice that the chooser understands, so the Oracle can predict them. There are a lot of smaller decisions which affect the timing (e.g., how many sentences Morpheus chose to say in his speech to the crews of the Vigilant and the Logos, which affected the timing of the crews' attacks to help Neo). Evidently none of these smaller decisions involved choices that weren't understood, so the Oracle was able to predict those as well. Furthermore, her instruction to Neo to "be [at Le Vrai], at that exact time" to deal with the Merovingian indicates that she is able to get the necessary timing right, even when it needs to be exact.
Note that the Oracle isn't necessarily manipulating all of these events, she just needs to pick the critical moments to affect. For example, she didn't need to manipulate the Merovingian to cheat on Persephone so that Persephone would help Neo -- she just needed to tell Neo the critical moment to ask for help, which was just after the Merovingian had upset Persephone by cheating on her once again.