Thanks for the quick reponse!
I think you might have missed the actual problem. I deleted the site and domain from ISPconfig, but it left pieces of it in certain places. After I deleted it, there was still the 'bad' domain name in /etc/postfix/local-host-names and /etc/named.conf still had the bad domain name in it.
DNS doesn't update at all now, even after pulling out the http:// domain name out of /etc/named.conf and /etc/postfix/local-host-names. I'm assuming it's still in the database somewhere that I can't see. I haven't modified the database by hand by the way. I'm by no means, a DBA.