I started with a Lyman tumbler. I think it is the Turbo model -- the one with the removable little window at the bottom to allow the tumbling media to drain out into the supplied pan.
Tumbler cleans brass just fine. The Turbo part does not work at all -- spills media all over the place.
Then I bought a tumbler from Berry's bullets. This one offered a separate rotary cage, like the one you may see at a bingo hall. You place the cage in the supplied clamshell, close the clamshell, and turn the cage handles back and forth. This catches all the media in the clamshell, and the brass stays in the cage. Works perfectly, and it comes with a clear plastic lid on the tumbler so you can see the progress of the cleaning brass.
I do believe that many different companies sell tumblers, but only a few companies actually manufacture them, so my Berry's may be the same thing as your Dillon, for example.
My advice: look for a clear lid; avoid the Lyman Turbo.