Except for the situation of being directly impacted by shockwave, the medium - air in this case - can't move faster than the speed of sound, ie the speed with

Except for the situation of being directly impacted by shockwave, the medium - air in this case - can't move faster than the speed of sound, ie the speed with which the pressure differential causing the movement is propagated. Once the fireball expanded and shockwave passed, the mushroom goes up because it's hot and thus it is moved by the atmospheric pressure. For example you wouldn't have mushroom going up without an atmosphere. It is able to go that fast because the whole surrounding volume was preheated by radiation and the shockwave with the resulting speed of sound increase .