I have an American Standard Shower with a single rotating valve that reads Hot and Cold and the valve is backwards. When I turn it to the hot, cold water come out and so on.

Sounds like the handle is on backwards, take it off, turn it 180 degrees, put it back on and see if that fixes it.

It is usually the cartridge that needs to be pulled, rotated 180 degrees and reinserted. Moen has their ccartidges label so you know how to do that in case someone plumbed their pipes incorrectly.