I thought the tampers and neutron reflectors were part of the core assembly in the early bombs? Need to go read the "Making of the Atomic Bomb" again, though I just reread it a rew weeks ago.
Criticality is dependent on mass, purity and density. You're thinking of a supercritical explosion. Criticality is simply a self-sustaining nuclear reaction. In a bomb, masses of radioactive material which would go critical if placed together, are split and kept apart. Then they are slammed together (very precisely) by explosives to shove them into a supercritical (explosive) state themselves. In a fission bomb, high explosives do the slamming (2 stages). In a fusion bomb, high explosives start a fission bomb, which then slams even higher potential nuclear fuel together into a fusion reaction (3 stages).
Every detail is misleading ~ they were keeping it secret ~ but ‘splaining why you could turn into a slow cooked crispy critter!