Just as tidal forces can push a moon outwards and over time, circularize the orbit, the planet's equatorial bulge has a similar force that draws the Moon into an orbit over the equator. This is true given sufficient time and enough rotation speed for the planet to have a sufficient equatorial bulge.
For a formation moon, there should be some similarity in the angular momentum during formation naturally. Similar to an impact moon like our own where the impact sets the planet rotating.
A captured moon can orbit in either direction with or against the planet's rotation at any angle to the planet's equatorial planet, at least, initially but the equatorial bulge has a tidal effect that over time, draws the moon over it.
Earth's tidal bulge, that moves the moon a few cm away every year is only a couple meters high over the oceans and a few inches over land. Earth's equatorial bulge is 42.77 km. Some 4 orders of magnitude more significant than the tidal bulge. It's not hard to see how a bulge of that size, over many orbits, would influence the moon into an orbit over the equator. The same is true for ring systems, which form over a planet's equator. "Ask an Astronomer" says basically the same thing.
Exceptions would be if the moon was recently captured, or if the planet rotated very slowly (Venus for example), or if the moon was close to the unstable region of the hill sphere where the object it orbits (planet) and the object that limits the planet's hill sphere (sun) both have an effect on the moon. I suspect (but I don't know how to do the math), that our moon's orbit being 5 and change degrees off Earth's equator is due to the proximity to the sun and Moon being no too far from the unstable part of the Hill Sphere.
The other moons you mention are much further inside their planet's Hill Spheres and much more governed by the planet's equatorial bulge. see table and chart below.