Of course wild animals move at their own will, and the wildebeest of the Great Migration move in accordance with the rains, which of course cannot be predicted (or only guessed to a certain extent).
You should be aware that the migration, whilst a wonder of the world and a spectacular sight for anyone lucky enough to witness it, is a much more static affair than many people realize. It is not possible to “follow” the herds, driving along with them, or even booking lodges, tented camps or campsites wherever they happen to be at any given moment. Of course all accommodation must be booked in advance and so this is not possible.
The famous river crossing is notoriously difficult to predict. It takes 1-2 weeks for the wildebeest to cross, and this can take place any time within a period of about 6-8 weeks. If it is very important to you to try, to maximize your chances of seeing this, we always advise to book for July, and stay as far north as possible in the Serengeti (where, at this time, only top-end luxury tented camps and a few private campsites that should be booked well in advance are located).
The most important thing to remember is that game viewing in Tanzania is truly excellent all year round. Even if you are not there for the migration there are resident herds all year round. Wildlife drama can, and does, take place all year round in Tanzania.