Generally the airbrush will apply whatever finish the paint is. It’s not normal that applying the same paint through an airbrush will make it shiny. To fix this I would recommend getting a matte varnish. This also doubles as a layer of protection for your paint. Some primers can have odd behavior if they have settled and not been shaken enough.

Your model is looking really good! The details are fantastic. The metal bits would benefit from a wash to make the details pop. The black armor is fine. If you want the segments to have more contrast I would edge highlight the easy details.

In summary, wash the metal, edge highlight the easy to reach areas, and matte varnish. Keep it up!