This answer to "How fast is fuel escaping a rocket for it to reach escape velocity 11km/s?" includes the following:
It can be seen in Figure 1.6 that the rocket can travel faster than the speed of its exhaust. This seems counter-intuitive when thinking in terms of the exhaust pushing against something. In fact, the exhaust is not pushing against anything at all, and once it has left he nozzle of the rocket engine it has no further effect on the rocket. All the action takes place inside the rocket, where a constant accelerating force is being exerted on the inner walls of the combustion chamber and the inside of the nozzle. So while the speed of the rocket depends on the magnitude of the exhaust velocity, as shown in Figure 1.6, it can itself be much greater. A stationary observer sees the rocket and its exhaust passing by, both moving in the same direction, although the rocket is moving faster than the exhaust.
I wrote the comment:
Your choice of quotes is excellent! "All the action takes place inside the rocket..." is the clearest most concise sentence I've read all year. This is an "Aha!" answer.
but now I'm having second thoughts about elevating the word "action" from an everyday word to its use in physics:
In physics, action is an attribute of the dynamics of a physical system from which the equations of motion of the system can be derived through the principle of stationary action. Action is a mathematical functional which takes the trajectory, also called path or history, of the system as its argument and has a real number as its result. Generally, the action takes different values for different paths. Action has dimensions of [energy]⋅[time] or [momentum]⋅[length], and its SI unit is joule-second. Action is only of interest when the total energy of the system is conserved.
Question: Can we say that this kind of action actually takes place inside a rocket along with the Newton's 3rd law action/reaction or "stuff that happens that's important and makes the rocket go" kind of action?
Illustration of Newton's "action" Source