As you can see in the below example, when a new user follows your account, you are notified as to whether you are already following them, their followers and following data, bio link, and recent updates.
If you want to message the user, just reply to the follow e-mail. This, in theory, could enable you to set up Auto-DMs from your e-mail, should you set up a rule. (But I wouldn't encourage it)
Topify is in closed invite-only beta right now, and is the brainchild of Ouriel Ohayon and @arikfr. You can get access to Topify with the following link for louisgray.com readers: http://snurl.com/doige.
You can find out more about Topify on their blog.