The post Junaid linked covers the basics of the functionality, but I wanted to address this:

then I have to sign out from several tabs

When you sign out of one tab, you should be signed out of all tabs within that browser. This is the behavior I see. For example, if I open two documents, then sign out from one of them, I can't perform any actions or load any new information without signing in. Even scrolling can trigger a login dialog.

As such, while it's a good idea to close these tabs after signing out from one of them, you do not remained signed in in these tabs.