To be able to send mails via different IP per domain, You need to do the following changes in the /etc/exim.conf file:

Find the “remote_smtp:” part, and add line

  
interface = "${lookup{$sender_address_domain}lsearch{/etc/virtual/domainips}{$value}}"

It should look something like:

remote_smtp:
  driver = smtp
  interface = "${lookup{$sender_address_domain}lsearch{/etc/virtual/domainips}{$value}}"

File /etc/virtual/domainips syntax:

domain.tld: ip.add.re.ss

That’s it. Create the domainowners file, restart exim, and You are all set!

pssst… If You want to automagically generate domainips file by IP addresses that are assigned to users in DA – check out this POST.