I took all your comments to heart, and I have come to
a conclusion, after further "study".

The "discovered" post-shave stubble IS related to the
cooling of the face. A cold-water finish and the application
of an alcohol-based aftershave did indeed result in the
skin tightening, which in turn revealed stubble.

However, on my face at least, this cooling process is not
immediate. It takes a few (5-10) minutes to occur.

Therefore, the solution (for me) is to wait a bit after
I'm "done", and then do a final touch-up on the shave.

Thanks for all the help and advice!

Cheers,
Paul