Just my experience.
I've never tried dishwasher detergent. Maybe I'll give 'er a whirl.
When I first got my Frankford Arsenal rotary tumbler, I used Dawn n Lemi-Shine.
For whatever reason, I got mixed results. Being careful and consistent with my proportions, the brass came out everywhere from bright white-yellow, to tawny orange-yellow (per batch; not individual piece variance). It was frustrating because there was no rhyme or reason to it - sometimes shiny - sometimes tawny. And nickel plated always came out dull and smoky-gray.
Then I tried RCBS ultrasonic cleaner, and the brass comes out perfect every time. Nickel still comes out dull gray though.
I have since learned the trick to nickel plated brass: Use luke warm water and just five drops of Dawn only (no Lemi-Shine). Comes out silver shiny.