I would have thought you would need to remove Lincoln before you can add and apply to Cardiff as you can only apply for one course at a time, but the fact they are offering you an offer before you have actually applied there seems a bit odd. In your initial email did you suggest that you were going to apply soon / had already applied? Are you sure it's an interview as well and not a talk about the course - i.e. it will be used to assess whether you get a place?
To answer your question though I would expect that you would need to physically apply to Cardiff through UCAS before they can tell you if you are successful or not.