Sounds like a case of the paint drying before it reaches the surface, in effect it's like blowing dust all over the model.
How much air pressure are you using and how far from the model are you spraying? If you're above about 18PSI, you're using too much air. If you're able to pump unthinned Tamiya acrylic through your brush, you're using way too much air.
Drop the pressure and get up close and personal. If your paint is running or spidering when you do that, then back off on the trigger and reduce the paint flow. You're using double-action brushes.
Though it works to an extent, don't thin Tamiya with water. It increases surface tension, induces separation in the paint and reduces adhesion. Thinning flat Tamiya acrylics with water can often result in a chalky, spotty finish, even if everything else is optimal.
Straight Iso works to an extent, but in hot, dry conditions it can contribute to the problem you're having. Tamiya's X-20A thinner incorporates a retarder to slow the drying of the paint and may help reduce this.