I don't tumble after resizing. I wash my resized brass in Simple Green and hot water in a sink.
I use a spray lube and quite a bit goes inside the neck so the neck is well lubed. A lot of media gets stuck inside the case when tumbling as a result.
I have tumbled and then washed and the amount of media that floats to the top is scary indeed.
Thats been my experience too with spray lube on large batches, small particles of media stick to the cases and no amount of tumbling will get the lube and media off. Dawn detergent and hot water does the trick. The only down side is it takes a 2-3 days for the cases to completely dry. Never really liked the oven on low heat thing.
On small batches I use Imperial sizing wax, and wipe off with a paper towel.
I ordered a kit that comes with a pad to roll the cases on and brushes to do the inside of the neck.