Control stays with previous app after four-finger swipe?
This is unexpected behaviour. There is no setting for this. Does this also happen when you switch to a different virtual desktop with the keyboard shortcut ctrl + left/right arrow key?

I would usually tell people to trash the plist that holds any related settings but it seems that com.apple.desktop.plist doesn't exist anymore in Sierra.

Installing sierra over the current install could mend your issue. Best to have the latest installer for sierra in that case and not an older version than you already have installed. This will, by the way, not delete you stuff. It will install the OS over whatever is already there. You can only loose stuff if you go erase the disk first before installing. 
Talking about re-installing, can you not install a later version of OSX? Maybe High sierra?