Hello 
The hourly mail limits are controlled with the following parameters in the /var/cpanel/users/username file for each account:
Code:
MAX_EMAIL_PER_HOUR=#
MAX_EMAIL_PER_HOUR-domain.com=#
Once those parameters have been edited, you should run the following commands:
Code:
/scripts/updateuserdomains
/scripts/update_email_limits
I also suggest reading the following threads, which contain more detailed information on this topic:
Max emails limit is per domain or per cpanel account?
Revert email hourly limits to previous behavior
Thank you.