We are running Exchange 2013 CU21 in Hybrid mode. Emails from Exchange Online users to Exchange On-Premises users is showing up as external. Transport rules that are supposed to apply only to external emails where "the sender is located" "Outside the organization" are erroneously being applied to emails that Exchange Online users are sending to the On-Premises users.
However, the emails from On-Premises users to Exchange Online users are showing up correctly as internal.
The header "X-MS-Exchange-Organization-AuthAs: Anonymous" is found in emails from Exchange Online to Exchange 2013 On-Premises users. When the emails are sent from Exchange 2013 On-Premises users to Exchange Online users, the header in the emails is "X-MS-Exchange-Organization-AuthAs: Internal".
How do I fix this, so that the emails are showing as internal both ways?