The synch belt people want 2 flanges somewhere on the pulleys/sheaves.
Some of our timing belts (mounted on shafts with real good alignment) have had a noticeable tendency to "track" one way or another, and flipping the belt reduced or even reversed the tendency to track. I think the manufacturer's catalog mentioned flipping as sometimes necessary to correct tracking issues
Flat belt pulleys are often crowned a little for good tracking (specs in machinery handbook, among others) but I'm not sure timing belts, which tug on the pulley major diameter, would like