Your arm angles.. Do static holds at each position. At the top --- A quarter of the way down (45 degrees) --- half-way down (90 degrees) --- three quarters of the way down (135 degrees) --- and probably a hold very close to straight arm.
The biggest trick for doing a muscle up on rings or bar is learning the false grip. It's a little different on bar and rings. Much easier to get used to on rings imo, though it's somewhat uncomfortable on each to begin. But it's really the only way to get a good muscle-up especially on rings. On bar, if one is strong enough you could theoretically release the bar at the top of the pull-up briefly to roll the hands, but it would be insanely hard. Much better to use false grip.