Airbrush is "spitting"...

That's ok Mike, sometimes it's good to double up an answer just to reconfirm. 

As Phil already covered paint can build up on the needle tip and then when you go and press down on the trigger (double-action airbrush), and it will spit that paint on the needle tip off.

Is this what you are seeing? If so, learn to spray along the path you are painting and after you have just come to the end of your painted path, keep the trigger pressed down but move the trigger forward and then release. This will blow off that little bit of paint that has collected on the needle. Another way to do it is to point the airbrush off in a direction away from the model and just shoot a second or two of air alone through the airbrush and then continue with your painting.

Sorry to be redundant Phil. I typed all this and then saw your answer was the same thing.

Often, spattering is a sign that the paint is not thinned sufficiently.

If the spattering is only occurring when you first start the air/paint flow and then becomes "normal", it's more likely an accumulation of paint on the tip of the needle, which gets blasted away (towards your model) when you press the button.

You can wipe, as suggested above and you can also get into the habit of starting the airflow with your airbrush ponted away from the model. Start the air and then bring your airbrush to bear on the areas to be painted. This works for most tasks, with the exception of spots/mottling.

 First off make sure that your paint mixture is as the consistency of milk. You said that you are shooting acrylic's, I have found that to keep a q-tip soaked in thinner and swab the tip periodically to keep the paint from drying on the tip of your "AB". Also keep a piece of cardstock handy to shoot your paint on before you shoot it on your model, this generally keeps from having accidents on your build.

                                                        Hope this helps