You have set the email address for cronjobs to send notifications to, but the cronjob is not sending the email.
If the email address is set for a cronjob, it will only send a notification if the script or binary that is being executed produces some sort of output.
The first thing to check is to make sure that the script or binary produces some sort of output when you manually execute it on the command line.
If you do find that it produces output, you should check the Exim logs to see if you can find the cron message details there. You can do this by using exigrep with the email address that you've set up for the cronjob to send to:
exigrep firstname.lastname@example.org /var/log/exim_mainlog