Your understanding is incorrect. When I restore in DisplaySpacesManager, it DOES move the Space to the appropriate display. The app just doesn’t go along with that space, and this is the problem.
I have 3 monitors, left, middle, and right. I have 3 desktops on the middle (primary) display. I have 4 desktops on the right display, and 3 desktops on the left monitor. I have the Mail.app assigned to the right display, Desktop #2. When I reboot, the middle (primary) display is unaffected, but the right and left displays do a switch. So now I have 4 desktops on the left display, and 3 desktops on the right. Apps that were assigned to the right display, desktop #1, now appear on the left display, desktop #1. Apps that were assigned to the right display, desktop 2, now are the left display, desktop #2. And so on, for Desktops 3 & 4. Conversely, Apps that were on the left display, desktop #1, are now on the right display, desktop #1. And so on, for Apps that were on the left display, desktops 2 & 3.
More specifically, the Mail.app has moved from right display, desktop #2 to the left display, desktop #2. When I restore the saved configuration using DisplaySpacesManager, the desktop configuration goes from 4, 3, 3 desktops on left, middle, right displays back to the original 3,3,4 desktops on left, middle, right displays, but the Mail.app remains on Desktop #2 on the left display rather than returning to the Desktop #2 on the right display.
As I said, when I am required to reboot, OS X switches the desktops from left to right and from right to left. But if I immediately reboot a second time, OS X switches them again so I end up with the configuration I want.
Let me know if you need further clarification.
Thanks for the great program!