I wet tumble, decap, then wet tumble again. It might sound excessive, but I do a few things that make it so it isn't.
If the cases have grit from falling in dirt, wet sand or mud, they can be rinsed first or wet tumbled for ten minutes and towel-dried. Even a quick wet-tumble should remove most of the residue except that in the primer pockets. Then they're ready to decap. I also use a Lee Universal De-capping die, but another option is the Frankford hand decapper. The reason I like the universal die is that I can use it with a press with a case feeder.
Here's why wet tumbling twice is not as much of a hassle as it might seem. After I've tumbled them a short time, rinsed and dried them (just a quick towel dry), I spray them with case lube, let it dry, and load them into a shell feeder on a progressive press. Now they're ready to decap, body resize, neck resize, and expand. Yeah, I use carbide dies, but case lube still helps significantly and the fact that I'm using a case feeder and accomplishing four die operations means I'm definitely not wasting time. Now the cases are fully formed, and the only thing missing is they need the case lube cleaned off and the primer pockets cleaned out.
This is when they go back into the wet tumbler. When they come out, they're completely ready to prime, charge, seat bullets, and crimp. All the resizing and mouth expansion is already done. This is also a good condition in which to store the cases since they are completely worked up to the point where the powder and bullet choice will be made.
If I only wet-tumbled them first, I would still have to decap them (load them onto the press or hand tool) and that operation is much less efficient since it must be done one case at a time, whereas tumbling can be done 1000 at a time. I also would have a dilemma about using case lube.
If I only wet-tumbled them afterward, I would be fouling my dies with grit and residue.
That's why I wet-tumble twice. I would rather repeat whole batch operations like tumbling than repeat individual case operations.