I use to use them A LOT also, but like Frog I have fewer problems now and don't really know why.
When I had a sign shop in another life, we liked Gershon WHITE tack cloths before the paint booth.... but that exact style seems to have disappeared. (Less sticky, less finicky.)
Yes, you can wipe very gently with any of them, but if you are careless or push TOO HARD just before coating with emulsion, you can transfer adhesive. I still use them on occasion, if it has been windy and dusty, or they have to sit too long before coating with emulsion. It does seem to help on those special occasions, and they get less tacky after a few uses.