I've seen this happen, even with friction shifting, when using a modern narrow chain with a crank designed for a wider chain.

A couple things to try: 1) as you suggest, perhaps the middle ring is backwards, although the counterbores for the chainring bolts make this difficult to miss. It would be an easy fix, if it is the case, though.


2) Try a wider chain. Are you perhaps using a 10 or 11-speed chain with your 9-speed cluster?