This is the response I was asked to post by Alex. The fix did not work and the regular logout button does not fully log you out.
Alex Posted the following
Try adding these lines, in this order, to the top of whatever module your modifying. I changed the javascript function call so that you can use this on the same page that you may be using the jfbclogin module, so update your onclick call to onclick="logout_button-click_custom()"
<?
require_once (JPATH_ROOT.DS.'components'.DS.'com_jfbconnect'.DS.'helpers'.DS.'facebookhelper.php');
JFBConnectFacebookHelper::init();
$fbClient = JFBConnectFacebookHelper::getFbClient();
if ($fbClient->user)
$logoutCall = "FB.Connect.logout(redirect_to_jfbconnect_logout)";
else
$logoutCall = "redirect_to_jfbconnect_logout()";
?>
<script type="text/javascript">
function logout_button_click_custom()
{
$logoutCall;
}