Someone else's Mac login screen

During the summer, I rented someone's apartment. She has iMac, which we could use if needed. I brought my MacBookPro, so I did not need to use her iMac. However, I used her Wifi (secured) with her ID and password. I realized when I turned on my MacbookPro, the login screen (where you input your password) had changed to the same screen as hers. When I went to Facebook, I got her account automatically logged in. The only way I could get into my own account was to turn off the "Do you want the password to be remember" function (I have never used that anyway).

Now I am back home, using our own Wifi. And I still have her iMac log in screen when I turn my MacbookPro on. I can change the login screen, but I am just wondering if this is common for two Macs to communicate each other without any permissions when using the same secured Wifi? I just want to make sure that all my accounts are safe and secured.

Thank you!