I use a squirt of whatever dish detergent is under the sink, half a teaspoon of citric acid, (found in the baking section at local supermarket-costs about $2, lasts months) and enough warm water to cover the cases and stainless pins by about an inch when horizontal. I use the slowest setting and one way for about an hour, check cases, perhaps another 1/2 hour if needed. It is important to get them out soon after they're finished and rinse in clean water. Leaving them in the dirty solution for extended period leads to tarnishing. I use the same process whether I'm tumbling pistol, rifle or cases from my big-bore black powder rifles. I've found it important not to overload these tumblers weight - wise. The slower speed stops cases beating each other up.
I de-prime all of my rifle cases prior to tumbling using a Lee universal de-priming die in a hand held press. I don't see the point in using a system that will clean primer pockets and not doing that. ( Although I can't be f#@ked doing it for small pistol cases, 9mm are just too finicky.

)
I tumble my brass so that it is clean
before running it through my reloading dies, clean cases = no crud in my dies.
I don't see any point in tumbling them afterwards. I wipe down every cartridge after loading as I inspect them with a cloth towel, so that gets rid of any residual lube. This can become tedious after a hundred rounds or so, but it satisfies my O.C.D tendencies when it comes to reloading.

P.S. I dump the rinsed cases onto a towel and roll them around to dry the outside after rinsing, that way I don't get water-spots as they dry. ( What was that I said about O.C.D?) 10 minutes in a warm oven in a baking pan will dry them out quickly if you need to load them straight away otherwise, I just leave them in the sun or near the fireplace on the towel.