I am thinking in terms of the Coriolis Effect, atmospheric circulation and specifically Hadley Cell latitudinal width here, but the base question still stands.
For ease of reference, if we take a satellite of a gas giant, assuming somehow it overcame the tidal lock, perhaps by a collision that knocked it around a bit, and started spinning in a retrograde rotation in orbit around the giant, would the absolute speed that it rotates increase or decrease relative to a base tidally locked spin when it comes to determining how physics like the Coriolis effect work?
If it was spinning faster then the Coriolis Effect would make more extreme longitudinal winds and banding, but if it spun slower then the Hadley cell would feasibly stretch all the way to the poles.
I don't know enough about physics to know which would be correct, unless it depends on how the planet developed a retrograde spin in the first place?