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I'm not sure if there's a trope for it, aside from Laughably Evil.
The leader of the Ax Gang (Kung Fu Hustle) does something similar. Not only does he have his own theme music, he actually dances to it as he shows up and immediately stops dancing when the music cuts off. At one point, he and his gang do an entire dance routine to it.
Edited by MiinU^ I figured it was a particular way of playing with the trope, if nothing else.
In the first part of this video in Ghost's background lore, Cardinal Copia enters the scene with music playing, but it's coming from the boombox he's carrying, which he turns off before speaking to the other characters. When he leaves, he turns the music back on.
I think there's at least a couple of different tropes happening here but my searches haven't turned up anything.