There seens to be another advertise company than the AirPush company that is using this ringtone thing.
AirPush, on its web site, offers its customer this kind of push advertising:
What type of ad units are available?
The ad notification action can vary depending on the Campaign Type you choose within the advertiser portal. The current campaign types and associated post-click actions are as follows:
Airpush App: launches the Android Market app preloaded to a market URL you specify.
Mobile Site: launches the mobile browser preloaded to a URL you specify.
Click to Call: launches the phone's dialer preloaded with a phone number you specify.
Click to SMS: launches the phone's SMS composer with a phone number and body you specify.
FAQ ... What type of ad units are available?