Is it possible to load Twitter.app instead of opening Safari when clicking Twitter notifications in the Notification Center?
The current behaviour really annoys me because it keeps making me sign in and I don't want it to remember my credentials.
Indeed, the Twitter notifications will always redirect you to the web application, even if you have a native Twitter client installed. In fact, Twitter notifications also work without Twitter.app as long as you have your Twitter account configured.
There currently is no way to change this behaviour.