Welcome to the ODK forum, @ouzoman ! We're glad you're here. When you get a chance, please introduce yourself on this forum thread. I'd also encourage you to add a real picture as your avatar because it helps build community!
What you're describing is the normal expected operation in Briefcase. Each time you pull a form, the new submissions are appended, and then if you export it, it will include the submissions that were pulled before, and the new ones.
I'm afraid that, at this moment, if you really need to create incremental CSV files, your only option is to remove the form from your Briefcase storage folder, as you've described.
We are discussing a new feature that would let you something similar here: Briefcase: Export from last