Apple ID log out

Hello,

Is there a way to log out my Apple ID on someone else's Macbook. The iCloud is theirs but the Apple ID is mine.

I have removed their device off of my list on appleid.apple.com but when I opened AppStore on their Mac, I keep seeing my account which bugs me a lot.

However, when I wanted to view the info for my Apple ID on their Mac, it asked me to sign in again. Does this mean I am logged out and they can log in with their account instead?

Thanks!