Some will say yes and some will say no, this is what I do.
When the temps are not to cold I tumble brass outside, and sift it through one half of an old minnow trap ( screen with small holes ) very handy and cost me nothing, also outside.
To control the dust I add an old dryer sheet ripped in half to the bowl while it's working.
Change it when dirty. For indoors I also use the dryer sheet AND KEEP THE LID ON (Duh)
Do what you need to do not to inhale the dust, it contains lead and other nasty things from the primers, DE-Primed first or not. So for the 5 Minutes it takes to get the job done--why not protect yourself with a little dust mask.
The nasty stuff is a slow kill, don't inhale it if possible, shooting is bad enough, specially indoors. Unless you have extra lungs in your shooting bag, protect the ones you have.
Stay safe and healthy.
Like Graywolf1, my tumbling is pretty much outdoors. My reloading/work bench is located in my garage very close to the side door leading to the outside. So even if I do work on my bench, I have a very large circular fan to remove smoke, dust, and other toxins to the outside. When things are a bit warmer, I also open the large garage door so the fan really does it's job unencumbered. Smithy.
If you hold your face over the tumbler and breathe the dust, it may have a detrimentaal effect on you. Normal handling is no more dangerous/toxic than vaccuuming your home. Yes, there may be lead dust from primers, but I believe you'll get more lead breathing city air...