Well, just my 2 cents. I think this multi-domain feature is built-in for Zimbra. However, I'm not sure what you mean by the last sentence: "mail be accessed from the primary zimbra account". Do you mean one user like John has 4 emails:
john@zimbra.company.com,
john@company1.com,
john@company2.com and
john@company3.com. And he just need to log in to the main zimbra account and see all emails? That's a little difficult. But I think you can use Zimbra Desktop to collect all those emails into one.
If John only has one email like
john@company1.com. Of course you can create a domain inside admin console, modify the dns settings, and he can log in from the mail server and check his own email, just use the full email name
john@company1.com as the user name to log in.