I am using Windows, and I have two monitors.
Some applications will always start on my primary monitor, no matter where they were when I closed them.
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So I agree there are some apps that you can configured to open on one screen by maximizing or right clicking and moving/sizing screen, then close and reopen. However, there are others that will only open on the main screen.
What I've done to resolve: set the monitor you prefer stubborn apps to open on, as monitor 1 and the your other monitor as 2, then change your monitor 2 to be the primary - so your desktop settings and start bar remain. Hope this helps.