The physical vibrations are caused by a pressure wave created in the air by the aforementioned super-heating of the air. If the pressure waves are strong enough, it will shake the windows when it comes through...just like the shock wave from a nearby TNT going off.
Sit near the front of a fireworks display. When you feel the "thud" in your chest when the big salutes go off, you're experiencing the same thing on a smaller scale. Same thing when near the speakers at a rock concert...in both cases you're feeling the pressure waves created by the explosion and by the