Fixed! After adding the ANE to all the build configurations under my Module Settings in IntelliJ.
I have about four different configurations, one for deploying to the emulator, one for the device etc and I had only added the ANE to the one deploying to the device as that was where I was interested in testing it.
But after I added it to all the other ones, I could resolve
import com.freshplanet.ane.AirAlert.AirAlert;
Hope this helps someone!