Yes, most sizable moons in our solar system are tidally locked (Pluto and Charon are tidally locked to each other, in fact).
Mimas orbits Saturn in a bit under a day, so that's probably the mechanism used, not rotation.
Alternatively, consider the possibility that unobtanium has the effect of somehow (*waves hands wildly*) nullifying the tidal bulge needed to do the locking. Or something. But if the moon is both rotating and orbiting, once every orbital period you'll have a very long night.
Dude. Floating mountains, 12-foot tall naked blue women. Who's paying attention to the damned plausibility at this point, anyway?