The bay is pressurized, with drop doors beneath each fighter. A ramp extends to the fighters individually, bringing on pilots. The bays are depressurized as the pilots (in flight suits) prepare. Then the drop doors open, the fighters pivot to nose-down position, and launch.
The fighters are in regular configuration when the pilot boards. Then the drop doors open, the ship tilts down on a massive pair of arms, and then they're released, the centrifugal force of the station sending them out the drop doors.
The starfury fighter is launched by a drop straight out, nose pointed "downward," toward space. Upon release, it flies pretty much straight out. still containing some of the momentum from the rotation, so it would appear to be going straight away from the station because its position in relation to the station, like a geosynchronous satellite, is still more or less correct. Shortly after getting out of the bay, the fighters fire up their engines. which lets them take any angle or direction they choose. So they can very quickly head away on any trajectory.
There is nothing wrong with the launch sequence. It causes them to move directly away from the station, on a slight spiral, facing out to the stars from the pilot's POV. Whether or not it looks funky has little to do with whether or not this is the most efficient means of doing this. I think it's kind of funky that the space shuttle flies upside down while in orbit, its cargo bay facing down toward Earth, but that's the way it's done, and there are good reasons for it. We sat down for a very long time with a bunch of designers and techies who know physics and know math and know flight dynamics. we ran computer models, and the physics are right.