How does a diver actually behave when the compressed air cylinder bursts?

I think that a compressed air bottle just tears like this is almost impossible. If, for example, due to poor screwing, rapid pressure loss occurs, a responsible diver will notice this relatively quickly.

What you mean is not a pressure equalization (that’s what you do when dipping, because of pressure on the ears – pressure equalization is always at “down”, whether exchange or in the plane when landing), except you have a reverse blockade, for example due to a strong cold (then you don’t dive). What you mean is the decompression stop. This has to be done by enriching more nitrogen under the high pressure in the blood and forming bubbles in the blood when it is too much.

As a rule, during sports diving, you can stay at times that you can spend on a certain depth in order to theoretically reappear without a decompression stop. Nevertheless, it is usually put in again during normal operation, sure is safe. However, if there is a situation where you have to show up due to a sudden lack of air, you have to go up, as soon as possible. Where each diving set is equipped with two mouthpieces, so that your buddy can also give you air (and even if there is only one mouthpiece, you can still change, so breathe in, hold air and pass over the mouthpiece and let the buddy take its train and then change again). Thus, an immediate ascent even with a safety stop/decompression stop would also be possible.

With such a safety rise, one usually learns to sing a kind of “uuuuuuuuuuuu” because one always exhales a bit evenly so that one tears the lungs when it emerges too fast due to the changed pressure conditions (a lot of air in the lungs through the large depth vs. less pressure on the outside). This is the much bigger problem. And should there still be any doubt that a decompression stop might have been necessary, it goes to the hospital in the pressure chamber. As I said, normally not necessary.