yeah but you're also assuming that they're subject to the same dimensions of time and space as we are
The signals still needs to get there so unless they have listening posts or are in the neighborhood the timing doesn’t match.
And in general the gamma burst form a nuclear explosion is so minuscule on galactic scales that it’s unlikely they can even pick it up over the background noise.
A spectral analysis of the atmosphere of the earth and the detection of fission borne radioactive isotopes is a much more likely method which means they would need to be actively observing the earth to detect it and still the same light speed capped timeline is in effect.
It’s not that they came here centuries after the nuclear tests, because even if they have FTL that is the shortest time frame that makes sense unless a nuclear explosion causes some signals that some how move faster than light which both violates physics as we know it and would be really unlikely to go unnoticed based on just how much data we have from nuclear blasts and nuclear reactors.