Delegated access applies only for full access; send-as, send on behalf or delegation from Outlook do not work. Cross-premises permissions do not work in OWA
This has been a major limitation of the Exchange Hybrid mode for quite long time.
I just noticed that you can now have access to a delegated mailbox hosted on premises if your mailbox is on Office 365, and the other way too.
I don’t know since then neither what is the prerequisites to get it working.
To give you a starting point, I’m running Exchange 2016 CU3 with Azure AD Connect version 1.1.281 (off course configured with the Exchange Hybrid option enabled)
The main mailbox is hosted on premises and the delegated is hosted on Exchange Online
The main mailbox is hosted on Exchange Online and the delegated is hosted on premises