I tumble briefly after loading to remove lube remnants from the cases, but I wet tumble before loading, so cleaning isn't really needed, just a quick degreasing (or de-waxing in my case)..+1 on photos, whatever you use don't use any cleaner that has anything ammonia based in it (Brasso, Simichrome, Flitz), and if anything cleaning it with a paper towel is better as it's a mild abrasive.
Side note I know plenty of re-loaders that will do a whirl in a brass tumbler once they are done re-loading it just may wear out your tumbler from the added weight.