To put it simply; the gas inside the flash tube gets very hot very quickly. (The flash tube itself will get very hot if the flash power and duration are long enough.) That causes the gas to expand rapidly, "hammering" on the flash tube. If the tube itself gets significantly hotter, that will add to the shock wave created in the air around the tube. It's the hammering that makes the pop, but there is also heat transferred to the air around the tube that can cause nearby membranes to react to the pressure.

When I was using large format cameras, very small apertures, slow film and very powerful studio strobes (several 2400 Joule heads within a light bank), it wasn't unusual for a subject to feel a puff of air at a distance of several feet. Not quite at the "vortex cannon" level, but a bit disturbing to some folks nonetheless. (Being in front of a camera is scary enough for most people; having the process literally hit you between the eyes does nothing for composure.) Part of that was the effect described above, and part of it was a very slight increase in temperature right at the surface of their skin causing some overpressure in the boundary layer of air around them.