When you normally move around the overworld, Link will transition screens a few pixels from the actual edge of the camera on the screen. If you turn coordinates on, you can see that transitions are activated on coordinates ending in numbers like
xx4 rather than something like
xx8 (the actual edge of the screen). However, through using out-of-bounds glitches and clipping, you can jump past screen transitions since the game will never properly run a transition while Link is airborne. If you jump past the edge of the camera, Link will wrap to the top of the screen he's on. But if you jump past the point a transition would normally occur but not quite past the edge of the camera, you'll have a FAWT armed towards the transition Link is partially inside of.
A Funny Auto-Swim Thing (or FAST) is basically the same thing as a FAWT but just over done over deep water. Because FASTs need to be done right next to screen transitions, Fake Flippers is an incidental component to performing them, and they can therefore be done without Flippers in Link's inventory.