In order to change the exim interface IP, do the following :
Editing /etc/mailips : This file controls the IP address from which each domains
should send mail. You will need to create and open the /etc/mailips file for editing using
your preferred text editor. You will need to configure this file in the following way:
*: 192.168.0.1 (<- desired IP )
Disable this option,
From WHM »Service Configuration »Exim Configuration Manager>>
Domain and IPs>> Send mail from account’s dedicated IP address "on"
And enable this option,
Reference /etc/mailips for outgoing SMTP connections.
And now, restart the exim service.