I do the de-priming and resizing at the same time, on the press after tumbling in Corn Cob media. Any media in the flash hole is pushed out by the de-priming pin on the die. I find this method to be very quick and very effective, but would never call down anyone who does it differently. We all have our ways.
I dry tumble vs. wet tumble due to the way I process brass. If I have a free day or half day, I grab a few handfuls of the pile of brass I have accumulated, tumble it, then process it, then re-prime it so that it's all in separate, back to back steps. That way I get that nice enjoyable, therapeutic( I think anyway) effect of reloading and not get bored with any one step in the process. By the time I'm done re-priming, the next batch is ready to come out of the tumbler and I start the process again. I typically get ~2000pcs done per day in this way. Wet tumbling involves a drying period for the brass as well as a media separation and equipment cycling process that would interrupt this flow, although I absolutely love the results it provides.
I have a primer pocket tool and typically only use it on Norinco 45ACP Brass(which is good brass btw), as there always tends to be some corrosion/oxidization residue on any brass I buy that has been wet tumbled. Let's call that 1%, and the other 99% of the tens of thousands of pieces of brass I've processed have never required primer pocket cleaning to have the primer seat properly. Hence, I have absolutely no problem tumbling then de-priming rather than the other way around.