That's not really how fallout works. Fallout occurs primarily when you detonate a bomb near the ground or the water, causing it to suck up a bunch of dirt/water

That's not really how fallout works. Fallout occurs primarily when you detonate a bomb near the ground or the water, causing it to suck up a bunch of dirt/water, irradiate it, and distribute it throughout the atmosphere. With a fusion bomb, you could end up with some leftover plutonium from the fission stage, but that's not the primary source of fallout.