It works because the crystals are actually just before the emitter and the ring around the grip is lined with conductive durasteel all the way around on both sides. This makes it so the power supply is always able to power the blade, and the emitter is much smaller than normal because the crystal is so close so the blade is refracted through a smaller hole yet is the same size. Also the flight part works by the lightsabers slicing through the air and heating up the air around it. We know lightsabers don’t give off heat but yet they melt metal and other materials and can cause wood to smoulder or burn. Because there is more air resistance due to that planet’s more dense atmosphere the blades are able to heat up the air, though just slightly. But, their rotation frequency is high enough to cause more heat than would be possible by spinning by hand. The inquisitors then use the force to keep that hot air around themselves (which causes lift) and control their direction by the force too. Because like Anakin controlling his direction and speed in AoTC when falling in Coruscant, we know force users can adjust their velocity (which is speed and a vector) to at least slow down enough to survive a few hundred foot fall. Therefore the inquisitors should be able to adjust their direction while also controlling the air around them to keep their lift.
I’m making this all up, I didn’t even make it past episode 3 of rebels and have only seen the helicopter video of the inquisitors.