First of all PADI does not do this exercise. They do the CESA, but not the buoyant ascent.
For PADI, this is done twice in the pool, and this description is what is supposed to happen. In my DM and AI days, I played the student in many a demonstration of this, and it never happened that way once. Every time it was done, I was breathing just fine and then got nothing at all. There was no warning. In contrast, when I have breathed tanks down (intentionally), the last breaths are indeed harder, and it is usually more than 2 harder breaths. The purpose of this is to teach the student to recognize that the feeling of a tank running low so the student can take appropriate action prior to running out completely. That action could be a direct ascent to the surface. Done at the first realization that the tank is running low, a diver should be able to make it to the surface without running out of air at all. That happens when a tank is running low; it does not happen (at least in shallow water) when a valve is turned off.