In order to receive the tweets as they happen you will have to have your Twitter Timeline contact open.

So open Contacts and find the contact named Timeline. This will open the IM window and it will update and then show the tweets from your Timeline. Keep this IM window open and you will get the new tweets whenever they happen.

This is a rather clever way of doing it. The user then gets to decide whether he wants to be alerted in real time about new tweets or not. This is probably quite useful for those who are following hundreds of Twitter users