You do not need a custom ROM for Titanium Backup, free or Pro. As long as you are rooted, you can use it.
When you purchase Titanium Pro, you have to follow the instructions in the email you get following the purchase (it will go to your PayPal email) and it will give you an authorization code. The email will explain what to do with this - I don't remember it myself. But anyway, once you do whatever you do with the authorization code, you unlock the "Pro" features. It won't be a separate app, just open it as you usually would the free version and you can access the additional functions.