The tumbler tends to leave a blackish dust on my cases and some of the primer holes have a grain of the media jammed in. This grain needs to be removed and the case needs to be wiped clean to avoid depositing the dust in the reloading die. For my .44 Mag. I usually only clean the primer pocket. My bottleneck cases go into the tumbler after decapping and resizing. That removes the lube reliably.
I also started shooting muzzle loaders. That removes need to mess with the brass completely.