Alex,
To get 'other' logout buttons to work if you have the Automatically Log Facebook Users In setting enabled, you need to add a little Javascript to the button itself. You can do this in the JomSocial template files, but I don't know the exact file off hand. If you need help finding it, just let us know exactly what page you're trying to use the logout button, and we'll try to track down exactly what template file it's in.
Once the link for logging out is found, all you need to do is add the following code inside the HTML anchor:
onclick="javascript:jfbc.login.logout_button_click()"
So, it will look something like:
<a href="/jomsocial/logout.html" onclick="javascript:jfbc.login.logout_button_click()">Logout</a>
Hope that helps,
Alex