I'm using Exim4 version 4.76 and can't really find what I'm looking for - except if I don't understand how exim4 works exactly.
I have configured exim4 as such that when we send an email from our web applications (which is on the same server as exim4), that it relays the email to a smarthost elsewhere - actually an email server that is owned and managed by one of our clients. Now, the problem comes in that when we send system emails (e.g. cron jobs that fail etc.) that it goes through our clients' mail server too, and we (and our client) do not want that. We want the system emails to be sent to our mail server (smarthost) and not our clients'. In other words, we would like to have emails sent to support@whatever from the server (local), be sent to our smarthost and not our clients'.
I hope this make sense.