Disabling the automatic start for teams and how to sign out:

Step 1: Click on your profile image on the top left side

Note: If you want to sign out of the application completely, select Sign out as illustrated below. 

 Step 2: Select Settings

Step 3: Under General, untick Auto-start application and On close, keep the application running. 

Note: By unticking On close, keep the application running the Teams application will close completely and will not continue to run in the background. 

If you want to keep teams running but only turn off notifications or silence them use this guide.