When you minimize a JFrame and then restore it, it's repainted. The question "What methods get called" is unfortunately a naive one, because keeping track of what is supposed to appear when is an extremely complicated process, but Darryl already provided you with the simple answer to what
you should probably do.
Although we haven't seen any code, so we can't be sure. It shouldn't take you that long to produce a simple piece of code which just has a JFrame and two JPanels, and subsequently makes one of them invisible.
I've found that making a component invisible automatically causes its parent to be redrawn, which results in that component disappearing and the other components being rearranged inside the parent. But that's my code. Yours apparently does something different.