Sadly, the default popup is a sort of internal frame (you can notice it has a different border than the confirm popup). It doesn’t seem to be a real popup, but just some sort of floating component inside the screen that always stays on top.
Perhaps you can try to create a genuine Windows popup like explained here: Single Vision Client on Multiple Monitors
Then it should be possible to set the JFrame always on top as explained here: https://stackoverflow.com/questions/297938/always-on-top-windows-with-java
Though it’s still very much a hack (as further comments explain)