The Twitter integration is like the iOS Twitter integration. You won't see notifications unless you have the Twitter app installed. The integration is so you can Tweet from OS X apps like Safari and Photobooth.
I'm curious as to how you tweet from within Safari? All the videos I see I never see them click a button or anything it just pops up. Is it illegal for devs to tell us how they have implemented it?
I saw that someone else but they say that button is to share links and such. Is that all you can do? I was under the impression you could just tweet whatever.
I just discovered that Twitter is already in 10.8 as an app.
No, it is not. My guess is you probably have it somewhere else on your hard drives (in my case it was on the Lion partition; I have ML on an external drive).