CiviMail sending to primary instead of bulk email account for smart groups

If I understand correctly, mailings should be sent to the user's bulk email account. They are being sent to the primary account.

Steps (I took):

1) Added an email address for my self and selected "Bulk Mailings"
2) Created a smart group for with just my self
3) Sent a mailing to this smart group

I received an email to the primary email, not the one that was marked for bulk.