Game closing (somebody "logging" into my account)

Since the update, I’ve noticed some suspicious logins to my account that weren’t me. Is anyone else having this issue? The game suddenly closes and says someone else logged into the account.

I imagine that just changing the password won’t solve the problem. I believe that if someone is already connected to the game, they’ll stay logged in because of Google Play or Apple. Is there any way to log out other people along with updating access credentials?