If you're skinny you probably won't gain a lot of muscle anyway but you will gain some back there. Mostly sugar in you blood will be used as fuel. When fat is used though it comes from overall bodies reserves and which is mainly from where your body wants to lose it rather than from the fat near the muscle. actually the fat near the muscle has nothing to do with where it comes off is what I'm saying.
Exercising your muscles burns fat while building muscle, so you will gain muscle in your glutes (butt muscles) while the jiggly fat part is what will go away, thus making your butt bigger overall but more shapely and round.
The best way to build the muscle is by using weights when you squat, as squatting by itself will probably just burn off fat mostly, as you said. You also need to increase your caloric intake in order to build more muscle. I'm no expert on the matter, but I've been trying to work on getting a bigger butt myself and that's what the sources say, lol.