The purpose of the Primary Domain Administrator user

When your email service is created, we create a user named "postmaster." This user is the Primary Domain Administrator. The Primary Domain Administrator creates new email users, establishes account quotas, receives system messages, etc.
It is important to check the Primary Domain Administrator's email often, as the mail system will send quota notices to that account (users approaching or over quota, domain approaching or over quota, etc.). For this reason we strongly recommend adding a "postmaster" profile to your email program to check the email box.
You can also set up your postmaster account to forward to another email address so you don't miss any critical system messages that are sent to the postmaster account.