I think these operate by beating a submerged ceramic diaphragm at ultrasonic frequencies, but no idea why that works (nor whether the effect occurs at the diaphragm itself or at where the ultrasound is directed on the water/air surface).
They use a submerged piezoelectric crystal somewhat underneath the surface of the water to broadcast an ultrasonic beam upwards. This puts high frequency waves on the surface, where surface tension causes some of the wave crests to pinch off into microscopic droplets that are propelled into the air, where they float around as mist. It doesn't heat the water, and it doesn't produce water vapor, which is transparent. They make lots of teeny tiny droplets which, if the sides of your container aren't high enough, will float outside the bowl and get everything around them very wet. They don't work well if submerged too deeply in the water, and they don't usually put out a large volume of mist like you'd see in a theatrical production (for that I think they use dry ice and it's a completely different process).