Here's the books description of exertion: A warrior requires willpower, whether born from discipline, survival instinct, or bloodlust, to control the ebb and flow of combat around them. Every call to act beyond a typical block or strike depletes this cool disposition.
Here's the section on exertion for the adept: At 2nd level, your training allows you to harness your mental energy into a supernatural state of focus. Some cultures refer to this energy as axé, prana, pneuma, or ki. Your access to this energy is represented by your exertion pool.
So... yes. You're right. Narratively, you decide how you can pull off your maneuvers. The term "exertion" strongly implies physical effort, but if you really wanted your fighter to be able to do these things because of magic, go ahead. And in fact, there are even magical combat traditions.