The best way to fix the brown residue would be to use a stiff bristle brush. I would suggest a stiff bristle brush like this:
https://www.amazon.com/gp/product/B000OCH8BI/
Spray the Wheel Cleaner onto the tires, then since your tires are already brown, I would suggest doing at least 2 rounds of hard scrubbing/rinsing with water, spray the cleaner again, scrubbing/rinsing, with the stiff bristle brush. This should get rid of all the brown parts.
The next step would be to thoroughly dry your tires, then hit them with our Tire Shine to rejuvenate and keep them protected.
For your reference, you can see all our available products here: CarGuys Amazon Store