Wow!! I've been using Tamiya acrylics for over a decade and I must admit I've never come across this problem. It's a real worry!!
I guess it's back to basics - clean the model thoroughly, use a good quality undercoat (flat white is often a good option, as it can warm up many colors like reds and yellows and requires less topcoat to cover), paint several very light coats before the first is completely dry, so the whole thickness of paint can dry as a single coat (if you understand my meaning). Or, let each dust coat dry completely for a couple of days. Try to make sure you don't use TOO much thinner for the paint - I use isopropyl alcohol for Tamiya - after all, you need the paint to flow through the airbrush but still need it to stick to the model, and don't use excessive pressure in the gun. I've had excellent results using Tamiya acrylics, "hot" acetone based automotive acrylics, as well as enamels. they all require slightly different techniques, but the general gist is the same - don't put on TOO much paint at once, and don't use TOO much thinner in the paint.