Attempting to play Populous on my old PC today yielded some interesting results: if you can call interesting the garbled mess coming out of the speakers when attempting to run the Adlib Sound version.
What picked my attention was that I also had a similar issue with Monkey Island 2. Back then, I just gave up as I couldn’t find any solution. When the problem presented itself again with Populous, this time I was able to find out more. So now I managed to solve it.
I was able to find the answer in a page of the Adlib Tracker II message board from 8 years ago. Some of the best ideas are buried that deep. Turned out that the SB16 requires changing the I/O 8-16 bit recovery setting on newer machines, such as my Pentium 3. I changed them (from 1-1 to 8-4) and now the game works like a charm. And so does Monkey Island 2.
Never doubt the internet. What you need to know is always available somewhere, if you know how to look.