Facebook is spooking me - privacy concerns

[Sarad AV]

hi,

 I have facebook.com logged in through one browser tab and http://www.cricinfo.com/ through another browser tab and was watching the scoreboard of the live match.  on looking closely, there is a small live chat area box within the cricinfo website discussing the game - where it identified my Facebook profile and had the facebook logout button on it. I clicked on the facebook logout button embedded on the cricinfo website and it logged me out of facebook on the cricinfo website as well as the facebook on the facebook.com website on the other browser tab.

probably this site is affiliated to facebook. i really donot wish to be identified through the facebook account when i choose to visit a website(which i might not even know is affiliated to facebook). however, there seems to be no way to disable this feature from facebook privacy settings. if anyone knows of a way to stop identifying facebook sessions on its affiliated sites, please let me know.

Thank you,
Sarad.