Exercising a particular muscle overtime does cause the muscle to grow (hypertrophy), and simply put, become more prominent though firmer.
Much of the bulge, however, can be due to the overlying fat. As such, muscle growth beneath the fat without appropriate attempts at losing the fat can indeed result in a more prominent buttock.
I would advise adhering to a good diet that is pro fat-loss, together with a lower weight, higher rep count and equally frequent cardiovascular exercise to promote fat loss and muscle toning. The lower weight count will also do your back a huge favour in the long run.
Regarding the question on squatting helping remove excess fats - it is not possible to deliberately target fat loss by area, lest you resort to procedures such as Radiofrequency ablation/cryolipolysis/invasive liposuction procedures. Toning, as mentioned, does happened and different muscle groups can be targeted depending on the squatting technique.
Safe exercising!
Best,
Shane
