[exim] Multiple domain query on DNS

I have a friend who wants to run Exim to support six domains. He's
currently using Exchange. Needless to say I'd love to help him out :)

But I don't know the answer to his question: right now his DNS is
configured such that a single IP address hosts a single domain, and the
reverse lookup comes back with the name of that same domain. He's
wanting to support additional domains on the same mail server on the
same IP address, which is one reason why he's interested in Exim, but
didn't know (nor did I) if he is supposed to have reverse DNS entries
for each of his new domains as well.

I hope that question actually makes sense, and that someone here knows
the answer.

Thanks,
John