Twitter live tile?

Make sure its enabled as a background task, perhaps reinstallation, repinning the app could help. And make sure there's live stuff to show.
 
Make sure to "activate notifications" in for the twitter accounts you want to get notifications for - I had to do this for all tweet souces manually since there is no "activate notifications for all my followed tweeters". It is not activated by default. You can also set it via the twitter website. This seems to be a filter somehow to avoid being flooded with notifications. :)