I'm not sure if there's a causation between using tire dressing and browning, but there are products specifically for cleaning tires.
I use Gyeon Tire Cleaner and their tire brush every couple washes:
https://gyeonusa.com/products/q-m-tirecleaner
Then I put on their Tire Express dressing which gives more of a deep black factory look than a cheap shiny finish.
My tires look brand new after 1.5 years.
Charles