Such stuff is usually a setting in the graphics driver on the system level. nothing to do with PS. You could only control it if you used a docked workspace.
Photoshop will open an image on the last monitor an image was on. If I open an image and drag it to one of my side monitors, then open a new image, it will open on the same monitor where the other image is sitting. If I open an image and move it to a side monitor, then close it on that monitor, the next image will open on that monitor.
So I think your answer is not correct. PS always opens the image on the last monitor where an image resided.
Have two monitors, A and B.
Open an image. It will open on A. Drag the image to monitor B.
Open a second image by double clicking an image in a finder window. It will now open on B.
Close images on Monitor B
double click a new image to open it. It will open on B.
Now take that image and drag it back to A. Close it.
Double click and image to open a new image in PS. It will now open on A.
Photoshop remembers the last monitor where an image was open, and will open subsequent images on that monitor, even if that monitor is no longer present. For example, if you open an image on your main monitor, then drag it to a projector window, then close the window. then turn off the projector. All new images you open will be on the projector, even if it's turned off. The only way to use PS again is to turn the projector back on, drag the images back to the monitor you want to use, then close them from there.
NB: To test your theory, I opened an image in Preview on monitor A, then dragged it to monitor B. Opened next image, and it opens on A. PS behaves differently than the system. This has always been the behavior of PS, from many version back, so this isn't specific to PS6, but it would be nice to be able to change or affect that behavior.