Hybrid Header preservation doesnt works

Hello!

One of my cloud tenant Exchange 2013 CU8 have strange problem.

After run hybrid configuration wizard, the cloud office 365 user send email to on prem, and on prem user see contact card and free busy info for Office 365 user. Header of this message is Internal.

However, If on prem user send email to cloud user, it has Anonymous in the X-MS-Exchange-Organization-AuthAs

In the SMTP log session, I see start TLS from the cloud server, see certificate exchange, TLS 1.2 negotiation and seems everything is normal. But this behaviour is very strange for me.

Any thoughts?

PS. In the other environment (EX2013) I didn't have this kind of issue- all works fine, as should be.