I dig into old document of firebase -
"Once a user authenticates to your app, Firebase manages their session, ensuring that the user is remembered across browser or application restarts. "
And in my testing of login in one browser with two tabs, they will share the same login status -- login or logging out at the same time.
Single-login plugin could not work perfect in this case. "Action:Logging out" under kicking condition will log out these 2 tabs. ~ hmmm
I will try to survey more detail about login configuration.