Realistically Trump is incredibly unlikely to have the basis to claim that with any certainty rather than just bravado. They're almost certainly in information lockdown now, so any unlikely intelligence informant with access would be under intense scrutiny and probably unable to report even the partial info they might have. And the bunkers themselves are a black box, from the outside there's little they can do to tell what's happening internally.

On the other hand the IAEA isn't going to have any useful data either. They've not got observers on the ground, they were all forcibly kicked out, so the only measurements they'd have are airborne radioactive monitoring stations in the surrounding areas. These are deep underground facilities that were targeted though, they're not going to be launching particulate plumes up into the air to be measured miles away shortly after. If there's any environmental contamination it will probably be in groundwater and take a while to filter out into accessible surface sources to measure. And that's still just an if, deep underground storage is the gold standard for radioactive waste disposal/storage because it's relatively disaster resilient and any containment breaches are unlikely to bleed up into biologically relevant areas.