I don't think it's possible to send messages to the official app from a different server. The application includes a couple of files called
GoogleService-Info.plist with information about the Airnotifier server, that's what you need to modify in your custom app in order to use a different server.
The reason it works like this is security. If anyone could use a custom server to send push notifications to the official application, it would be possible to impersonate others. So everything needs to go through our Airnotifier server at some point.