When I spray welding projects or car/tractor repairs with urethane paints and a full size spray gun, I always wipe them down with solvent and then a tack cloth to remove dust.
Do you do a similar prep with models and airbrushing acrylics, or does the wax in the tack cloth interfere with paint adhesion?
I personally hit my parts with a quick blast from a canned air duster right before painting. For me, tack cloths have had a habit of depositing more gunk than they remove, and they also make it really easy to break things off your model.
I use paper towel wet with liquid that depends on the paint. I use paint thinner for oils, alcohol (56%) for acrylics. Not too wet- not dripping, but damp. I used to use Kleenex but found it leaves lint, which the paper towels I use do not.