Article briefly talked about delivery, which is tricky to do precisely at best of times, but didn't really mention how to address delivery into a nuclear blast. Hundreds of meters behind the craft about once a second doesn't seem like it would be enough time for the blast to clear so would get in the way of sending a new capsule backward. Anyway I'm sure it's just an implementation detail
In a vacuum, there isn’t a fireball hanging around for the next charge to cross; the plasma is moving outward at thousands of km/s.
A lot of the work was done to a design point of 0.25 seconds, and Dyson's book says the issue there wasn't the blast clearing, but just being able to move the machinery fast enough. I kind of share your puzzlement; I can see the blast clearing this quickly in space (the debris moves at tens of thousands of km/sec) but not in the atmosphere.