Even though I have enabled auto quitting for Steam and Uplay launchers, if I go to the installation of the game that is associated with a 3rd party launcher, then quit the installation, or in the game for just a few seconds then exit the game, these 3rd party launchers won't auto close. Is there a minimum amount of time that I must be in the game of the associated 3rd party launcher for the auto close feature of the 3rd party launcher to kick in?

Try asking in the Galaxy Forums (You'll probably get a better response there):
https://www.gog.com/forum/general_beta_gog_galaxy_2.0#1609534331