Boomla has a central login system. If you log in on boomla.com, you will be immediately logged in to all your Boomla websites. Same goes for logging out, you have to do it, centrally, on boomla.com.
For example, potato.boomla.net is my website. To log in, I click the Login button, which brings me to boomla.com. I log in.
Refreshing potato.boomla.net, I’m logged in, here too.
To log out, I go to Control Panel, Logout, log out. Refreshing potato.boomla.net, I’m logged out here too.