Can't receive emails if I only set up an MX record

==== Required information ====
- iRedMail version (check /etc/iredmail-release): 0.9.2
- Linux/BSD distribution name and version: Ubuntu 14.04
- Store mail accounts in which backend (LDAP/MySQL/PGSQL): MySQL
- Web server (Apache or Nginx): Nginx
- Manage mail accounts with iRedAdmin-Pro? No
- Related log if you're reporting an issue:
====

Hi,

Here is what I'm trying to do:

My mail server is mailserver.domain.com with IP 111.111.111.111

In domain.com, I have the following records:

A         mailserver.domain.com    111.111.111.111
MX  10 mailserver.domain.com

This works, no problems here.

I set up a second domain (second.com) and set up the MX record for second.com like so:

MX 10 mailserver.domain.com

I did not make another A record for second.com thinking that pointing the MX record to mailserver.domain.com should work.

I don't receive any emails to second.com using that set up.

However, when I do the following, it works:

A mail.second.com    111.111.111.111
MX 10 mail.second.com

My goal is to only change the MX entry of second.com to "mailserver.domain.com" and make it work. Is this possible?

Thanks,
Chris