Are you using the "Aqueous Hobby Color" paints (similar jar to Tamiya, Paint numbers have a "H-" prefix) or the "Mr Color" paints (lacquer based, jar has a lid which narrows to a paddle-like shape at the top, paint colours have no prefix, just a number)?
The aqueous colours should be compatible with Tamoya acrylics - the "Mr Color" lacquer based paints won't mix - it sounds like the latter. If this is the case, you will need to run some lacquer thinner through your airbrush and perhaps strip it down to clean it up.