To log out, click on your name / avatar at the top right, and select 'Log Out' from the menu entries.
It looks like XenForo does not automatically log you out (and there is no configurable item that will make it that way). It will just not show you as 'online' if you have not been active on the forum within the last 15 minutes.
And, it defaults the 'stay logged in' box to being checked.