How does a rocket push against its exhaust? Does the reaction come from the rocket nozzle or as a result of the imbalance of forces in the combustion chamber?
Yes, the imbalance of force in the combustion chamber explain how a rocket works. The hot expanding gases push against the top of the chamber, but not the bottom since it's open, and so the rocket is pushed upward. (The gases push against the sides too, but those forces balance each other out).
That's just the gist of it, though. The shape of the nozzle is very important to the performances of the rocket. If there was simply a hole at the bottom of the combustion chamber, the gases would spray out in every direction, carrying a lot of wasted momentum with them. But by pushing against the nozzle, which redirects them downward, more of that momentum is transmitted to the rocket.