When I hit "OK", the "addActionListener(ActionEvent e)" method of my parent JFrame is called
Technically, the addActionListener() method was called as the GUI was being built, before it was displayed or made visible. Selecting the "OK" button runs the actionPerformed() method of the attached ActionListener class, which in the case you provided is the current instance of 'this'. Is 'this' a reference? Of course, a symbolic one, and one we can't use that to derive a pointer as one can in the C languages.
Am I actually just constantly making new copies and manipulating those?
That's probably an over generalization or simplification, so I'll say "No," but show some examples of what you have in mind. And in this sentence and the next, I'm not sure what you mean by 'manipulated/ing." Try to use a more precise term.