I could be wrong, but I don't think the Facebook tile on the Band is compatible with the beta version of the phone app. What I think happens is that when your phone gets a notification, the Health app looks at the app name for the notification. If it's one that you've enabled a tile for on the band, it makes it show up there. Otherwise it just puts it under the general notifications tile.
I believe the internal filter for Facebook is looking for notifications where the originating app is called "Facebook." For beta users, the declared app name is "Facebook Beta," and therefore it doesn't get caught in the filter and ends up in grouped with the other uncategorized notifications. Which is why it looks like the Facebook tile isn't doing anything.