Such "radiations" have happened every time when there was little competition either because a new place or environment was invaded or because a catastrophe had eliminated the former incumbents.

The result of evolution "radiations" was that some group of animals that previously had been more or less uniform because they were adapted to a certain niche, after the "radiation" event became diversified in a large number of groups adapted to very different conditions of life and having much less resemblance between themselves than before.

However, the same risk applies to "explosion".

It is probably better to not use metaphors like "radiation" or "explosion", but to just say something like "diversification event".

However, "radiation" already has a long history of being used in the biological literature with this particular meaning, of divergent evolution, so for those familiar with the jargon, it seems an appropriate choice, even if it might not be the best word to use in something intended for the general public.

The "radiation" events are not events when the rate of mutations was higher (even if it is likely that the mutation rate during Cambrian was a little higher than today, due to higher ambient radioactivity because less of the primordial radioactive nuclides had already decayed by then).

The "radiation" events were events where a much larger proportion of mutants survived enough to have descendants, because of less competition that would have otherwise eliminated them.

This allowed a chain of neutral or bad mutations to lead eventually to improved organisms for certain conditions of life, while in the times of high competition it would have been impossible to escape local optima.

So while the rate of "raw" mutations was about the same as in other times, the rate of successful mutations, that persisted in the DNA of the descendants, was higher.