The only way for something to send messages and not have them appear in exim_mainlog is for them to be sent direct via port 25. Either cpanel or CSF have the ability to block direct port 25 outgoing email and your should ensure that it is ALWAYS blocked (as you can't log it, and spammers love to use this bypass).
You should be grepping exim_mainlog for something like:
Code:
grep '=>.*@yahoo.com' exim_mainlog
which will tell you what emails are being sent to yahoo. Replace "grep" with "exigrep" to see the entire log message for each message.