Your car is picking up dirt on the way home from the wash. Simple as that. That coupled with a touchless not actually getting the car 100% clean, that is where your swirls are coming from.
Like others have said, use a rinseless after the touchless, or skip the touchless all together.
For you detailers who are an authorized installer, what is needed? I consider myself a professional part-time detailer, but I mainly just work on friend's and family's cars. I'm thinking about setting up an actual business this year and have been doing some research.
I've used Cquartz before...