I coated my tires as well with DP Tire Coating (now McKee's 37). Soap, a mothers tire brush and water is all I need if I do a bucket wash. Or a wipedown with a dedicated set of microfiber towels for wheel and tires when I do a rinseless wash. The coating keeps the dirt from penetrating into the tire. It also keeps the browning from building up from within the tire. It's like having a layer of clear on the tires. Either wash method is all that is needed.
I simply recoat the tires when they are in need of a fresh application. Right now I am at 4 months with DP Tire Coating that has been proved to be pretty durable. Was testing to see how long I could go without reapplying so I can get an idea of how durable the tire coating is. I am starting to see areas where the coating has begun to come off. I will be recoating them sometime over the next week.
Also a tire cleaner won't completely strip the DP Tire Coating in one shot. Especially if it's fresh. Trust me I tried. Nick provided me with some valuable information on what will actually remove it.
Saves me a lot of time and work having both wheels and tires coated. Same can be said on my dad's Impala which has the same combo.