No, you don't need any other reverse DNS for additional domains. It's only necessary for the IP address that the server is on and the domain which is the primary domain on the server.
I forgot to mention earlier, while you're waiting for a resolution to this problem you should be able to relay your email through your ISPs mail server. That will ensure you don't get on any RBs or blacklists. The configuration for this is in the Admin UI, if you need to authenticate your server then follow these instructions in the wiki:
Outgoing SMTP Authentication - Zimbra :: Wiki