Did you disable notifications for them? Settings > apps > FB/Twiiter > a checkbox near the top.
Facebook is pretty notorious for being a horrible app. I am not entirely sure it has been updated to play nice with ICS yet, so JB I would have my doubts about as well. I don't use FB though, so I can't really comment, just echoing things I hear about it.
While I use Twitter, I don't use the official client so I can't say much for it either (also I don't use push notifications, I follow way too many people haha).