What USC are you using?
Assuming you have something fit for purpose, either a citric acid mix or some sort of acid additive along with warm/hot water and a squirt of fairy liquid is what is needed.
I use 50/50 ratio of warm/hot water and distilled vinegar (bottles are about 25 pence from tesco which will do a cycle of 50 large cases or 100 small) My USC has a heater which is also useful but if yours does not, put hot water in there. I then give it an 8 minute blast, remove the tray and give it a shake and then give it another 8mins. That is all I do. Primer pockets are generally spotless but some will have the tiniest bit of scum still attached. I am more interested in cleaning the internals of the case and the neck prior to annealing rather than the primer pockets.
Once done, be sure to rinse the brass well in plain water and I also leave mine to soak in a bicarb of sod mix for a handful of minutes to help neutralise any remaining acid on or in the cases. I dry mine in the oven on a low temp (about 120 degrees) for 10 mins but you could leave them to air dry or do it some other way. Your cases will be dull and not shiny like a tumbler but I don't care about that cannot be bothered to have brass rattling around for hours no end for no actual benefit. That would be up to you.
Something I never thought about before is the type of water supply folk have and whether that makes a difference. I live in a soft water area which is good for having a shower or bath. The soap lathers up easily and the water seems less harsh on skin than when I lived in a hard water area. I think I prefer the taste of hard water. Anyhow, I wonder if that has an impact on how well USC's work?