The fission reaction, which is required for the atomic bomb, is kept "in check" (non-reactive) by keeping the nuclear material at sub-critical mass, meaning that the mass is at a lower density than what is required to sustain fission. The atomic bomb design is based on implosion, so explosives are placed as the outer layers of a sphere of material, and the nuclear material sits at the center of the sphere, to be compressed when the explosives detonate and thus reach critical mass. In other words, there is nothing really holding the "pressure" in an atomic bomb; the pressure of explosions/implosions is simply not generated until impact.

Nuclear bombs don't explode on impact. They explode when they are triggered. This is because the explosion has to happen in an extremely controlled way or else the fissionable material making up the core of the bomb will not be able to sustain nuclear reactions, and you will not get a nuclear explosion as a result. Blowing up a bomb that would normally be nuclear on impact would result in radioactive fissionable material being strewn around by conventional explosives.