PA24 Comanche - alternator belt "flipped" in flight

1962 PA24 just annualed and a new alternator belt was fitted as prop was
removed. The new belt looks different from the old, but the part number (I
am told) was supposed to be matched/equivalent. The new belt has "teeth" as
it were. The old one was just a standard tapered belt with smooth surfaces.
On a 3 hour flight back to base the belt flipped over. It now has the teeth
facing outwards. It is probably lucky it did not break.
Fixing the problem will require removing the prop unless it is the correct
belt but was somehow not correctly adjusted. (It was the correct way around
on pre-flight and tension seemed correct too.)
Has anyone come across this new belt, and had any similar problems? To my
mind, we just need a belt that looks like the old one. I suspect they are
not compatible, but the mechanic says that according to part numbers they
are.
Any info, appreciated.