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.