Cmd+Tab breaks "Assign To This Desktop"
The apps are not being moved to different desktops, but the desktops are being rearranged. To see the difference, put two apps on a space, then Cmd-Tab to one of the apps.  You will end up in a space that contains both apps, although the space will have been renamed and shuffled in the order.

To stop this, 


Open System Preferences
Go into Mission Control
Uncheck Automatically rearrange Spaces based on most recent use