I use two external monitors connected to my closed MacBook Pro. When I use Royal TSX it is in Full Screen mode on the second monitor.
When I restart the OS and when I restart Royal TSX it appears in Full Screen mode on the first monitor. The expectation is what it will stay on the monitor it is initially assigned to.
Other applications I use such as Airmail, and Apple's Numbers will follow this convention.
I'm experiencing the same issue all of a sudden. I've used the method you are showing in the screen shot, but it still defaults to the screen that is not highlighted with the red. The only way it seems to let me have the full screen on the monitor I want is by going to mission control and dragging it to the monitor I want. Prior to this issue It would always open to the desired monitor. I tried the beta as well and still not working.
I don't think the issue you're describing is related to anything in this thread.
Could you please open a new support ticket including a short video that shows how your connection is set up and what exactly is happening?
I'm closing this thread as the original issue has been resolved. If you still encounter a similar issue, please open a new support ticket or forum post.