I have a personalized email (username@domain_name) setup using Outlook.com and I am receiving mails from all other sources except from wordpress@<domain_name>.
I tested by sending mails from following:
Gmail=> Works
Outlook (live.in email address)=> Works
Outlook (custom_domain address)=> Works
Yahoo=> Works
But E-mail never appears when there is a notification from Wordpress or Using contact form configured to receive e-mail on name@<domain.com> (Where name@<domain.com> is setup using Outlook.com), Although it worked when i changed mail to my gmail address for testing.