I think this dual-meaning for 'after' is quite common, at least in Ireland and UK (and Australia). Here's an example in lieu of a formal citation:

1. After getting dinner, Alice and Bob met friends at a local bar - Purely temporal, one thing followed the other

2. After hearing Alice recommend her gym, Bob signed up for a membership. - Causal (and temporal of course): because of the first thing, the second thing happened

You can disambiguate this in many ways, the most common in my experience is to make explicit the time

"Darwin discovered the theory of evolution many years after studying finches on the Galápagos Islands"

I don't think that's different meanings of after, but different typical inferences that a listener might make.

You can see the same relationship more clearly in the word since, where the causal sense is much further along.