There is a common problem with most hostings, when you setup Google Apps for serving the emails for your domain and you expect to receive notifications from your web application in the mailbox. The issue is caused by the “Local delivery” case. When sending emails from the code and the target is a mailbox in the same domain, the MX records are usually not checked, but the mail function tries to deliver the email locally. What happens is it does not find the recipient, so the email is lost.
What should be done is setting up the email routing to “Remote mail server” in cPanel at the MX Records page. Additionally it’s a good idea to add all MX records from google in cPanel even if you have the DNS hosting somewhere else.