The devil is in the details, and there are many details that I don't know, but...
Once the generator is in synch with the bus, it will tend to stay synchronized.
If the generator were to try to speed up, then the electrical power output of the generator would increase. This will result in a corresponding increase in torque demanded by the generator.
If the generator were to try to slow down, then the electrical power output of the generator would decrease. This will result in a corresponding decrease in torque demanded by the generator.
The change in torque acts in the opposite direction of any speed change; the net result is that the generator simply stays synchronized. If you were to simply 'cut out' the prime mover entirely, then the generator would start acting as a motor to maintain shaft speed.
You can imagine the entire grid as a large flywheel, and the generator as a small flywheel coupled to the large flywheel through a spring with some damping. With changes in load, you get small changes in the relative angle between the two flywheels, but the overall speed stays the same. If the small flywheel tries to fall out of synch with the large flywheel, the spring pulls it back to equilibrium.
With asynchronous (induction) generators, you do get speed changes around synchronous; but the net result is essentially the same.
The complexity comes in when you get stuff like hunting and subharmonic oscillations, where the mechanical system is exchanging energy back and forth with the electromagnetic system, or exchanging energy through the electromagnetic system between generators. You can imagine how a sudden change in load might make the small flywheel oscillate around its equilibrium position....