My boyfriend keeps receiving my facebook notifications on his Macbook. How can this be deleted?

Right before I became a Macbook Pro owner I used my boyfriends macbook for everything. I had my own page to sign in so it wouldn't conflict any of his work... When I finally I got my own macbook I noticed my facebook notifications would come up on my mac and my his mac as well. I don't know why he is getting my facebook notifications, but its kind of annoying. He even thinks so even though he is able to watch my every move lol. not really though... but anyways, he said he deleted my guest page and everything, but its not working. what is he doing wrong?