Unfortunately it is a broken functionality that seems to assign an app to a specific desktop rather than the one you chose, and I've not either seen the option to assign to a desktop more than once.
For example I have my email program on desktop 10 on my second monitor. Under Options it only specified Desktop on Display 2. After each screen save event it would remain there even though most other windows would be on display 1. After the latest update (13.1) it looked like they fixed finally that with all apps still appearing on display 2. But what it did was place the email window on desktop 9. Under Options it also said
After the latest update it said Desktop 9 on Display 2.
If it does work every time then it must be so obscure as to being just as broken. Though I greatly appreciate the effort by @dialabrain who have clearly seen some kind of workability here.
OK, so while typing this I've been messing around with the above and I noticed that now my email window is listed as being on Desktop 10 on Display 2. What I had done was shifting the second display to a different desktop and checking the Options settings on various icons.
Whoa, I decided to repeat with Chrome for Google access (of which I have two windows open) and belongs on Desktop 9 Display 2. Options said None which I've concluded must mean No specific desktop. But when I clicked on Display 2 and the two windows jumped to Desktop 7.
I found that when I try to change the desktop assignment it picks one nbr lower than where it is (and where I want it). I'll try to follow up here if and when I get it figured out.