I'm having the following problem..
All mails get to Zimbra accounts without problems except the ones that are sent from the server that has the account using it's domain.
Let me explain how we have set-up our server:
We've created a VPS and installed Zimbra Server on it (has it's own dedicated IP).
On a totally different dedicated server, we've the hosting account which uses the domain that we want mails to be delegated to Zimbra (so we set-up the corresponding MX record pointing to the Zimbra server). All works fine and mails sent from gmail, hotmail, or any external server get to the Zimbra server. But the problem comes here. All the mails sent from the dedicated server (where the domain is being hosted) are being sent to the mail accounts that we previously had (configured on cPanel) instead of being sent to Zimbra.

What should I do to avoid this? And so that my mails (sent from the local server) are not sent to the old mail addresses configured on cPanel (which are on that same server) and are sent to my Zimbra server.

Let me know if I didn't explained myself correctly or you need any other info-