Boomla has a central login system. You do not log in to individual Boomla websites, rather you log in to the entire Boomla Cloud. Logging out on boomla.com also means that you will be logged out from all Boomla websites.
It's easy to tell if you are logged in or not on a Boomla website:
If you can NOT see the Boomla Toolbar you are NOT logged in.
If you can see the Boomla Toolbar and it has a Login link on the right, you are NOT logged in.
Otherwise, you ARE logged in.