For postfix I can change the binded ip by changing parameter like
smtp_bind_address = 192.168.146.197 in main.cf
How to change the ip address binded by zimbra(server have multi ip's) ?
You can do the same process editing the /opt/zimbra/postfix/conf/main.cf (like root).
So restart postfix with zimbra user
and must work like you need.
For Zimbra 8.7: