The (very) short answer to your question is that paintComponent is called “when it needs to be.” Sometimes it’s easier to think of the Java Swing GUI system as a “black-box,” where much of the internals are handled without too much visibility.
There are a number of factors that determine when a component needs to be re-painted, ranging from moving, re-sizing, changing focus, being hidden by other frames, and so on and so forth. Many of these events are detected auto-magically, and paintComponent is called internally when it is determined that that operation is necessary.
I’ve worked with Swing for many years, and I don’t think I’ve ever called paintComponent directly, or even seen it called directly from something else. The closest I’ve come is using the repaint() methods to programmatically trigger a repaint of certain components (which I assume calls the correct paintComponent methods downstream.
In my experience, paintComponent is rarely directly overridden. I admit that there are custom rendering tasks that require such granularity, but Java Swing does offer a (fairly) robust set of JComponents and Layouts that can be used to do much of the heavy lifting without having to directly override paintComponent. I guess my point here is to make sure that you can’t do something with native JComponents and Layouts before you go off trying to roll your own custom-rendered components.