Wrasses such as sixlines and leopards will compete with the mandarin for pods. The flashers, fairies, etc really don't cruise the rocks looking for pods. Those should be fine with a mandarin.
There are also some fish with some red, like the Swissguard Basslet, radiant wrasse, etc.
But IMO, the best red fish has to be a Cuban Hogfish. He's reef safe, minus shrimp, and would fit well in a 125gal.