Logging out from my site doesn't detach the FB user

Well, I try to describe the behavior:

In my application, the user logged in using facebook. There are some pages where he can submit comments or see comments of his/her freinds.
I use {JFBCComments href=http://www.boutique-annab.com width=550 num_posts=100}

Now, if I push logout, the user is disconnected, but he is still active on the comment area, and his friends' comments doesn't disappear.

I think this should be a bug.

You will find attacched:
1) a site page with cache cleared (both browser and joomla), before the user sigfned on

2) a facebook login page for the user

3) the page with the friend's comments

As you can see, the login worked fine ( the user photo and name on the top right corner) and the list of comments on the page bottom.

Now I press Logout, and the application redirect me on the Home page as configured. There is no user logged in.

4) If I return to the detail page there is the error: the username and password are empty as the application should be ready to accept a new user, but on bottom, there are still the message for the user logged out. These info should not be present there.
Please, note that the access button for facebook is not the same as in the first attachment.

Thank you

Paolo