Weird Gmail Notifications Happening--Help Requested

[Pseudo-Fed]

Had been using the Gmail app for my work account, with special authentication required (a gsa.gov account). I logged out and logged back in as my gmail.com and get my messages fine. However, I still get badges and sounds each time my gsa.gov account gets mail! I even deleted the app and reinstalled and logged in to my personal gmail.com account.

Any idea how to get the app to stop delivering sounds and badges for the account I'm not logged into?! Thanks.