Hello Öykü,
Yes, this is expected when running multiple final versions. Since preferences are stored in the same place, you’ll be signed out. It doesn’t matter if you keep one app closed, you need to quit it and run only one final version at a time. You can keep multiple final versions in your Mac, but you can only run one at a time.
If you want to work simultaneously on 101.9 and Athens you can use the beta. Beta versions store their information in a separate place, so you can run both without any issue.
Just keep in mind that beta versions are under constant development and there may be some bugs, so having a backup of your files is always recommended.