There's no generic API that tells you when someone has pointed their nameservers at your server.
But there are two ways you can discover that information without anybody notifying ("pinging") you:
1) If someone's pointed their nameservers to you, and then someone tries to access that domain in any software, it's going to result in your name server getting a DNS query to resolve the domain. Hook into your local nameserver somehow (depends on what DNS daemon you run) and you'll know about new domains you're being queried for. Do your own DNS lookup to find out if you're listed as authoritative for those domains.
2) Get access to the .COM, .NET, .ORG etc. root zone files. This is harder, since AFAIK it's only given out with permission by the companies that run those registries. If you can get access, you can poll the file for new domains listing your server as their nameserver.
Your admin had probably done #1. Here's some info about telling BIND (the most common DNS system) to log its queries: http://www.cyberciti.biz/faq/howto-enable-dns-linux-unix-server-logging/
Once you have that, all you need is a script to watch the logs for domains you haven't seen before.