So, in my lab I have Exchange 2010 and Exchange 2013 in coexistence.
On the Exchange 2010 box I can run Search-AdminAuditLog and get all the CMDLETs that have been run in my environment. Including CMDLETs run from the 2013 side. As expected.
When I run Search-AdminAuditLog from 2013 EMS it returns no results. Just goes back to a prompt as if the AdminLog was empty. No error.
The configuration of the Admin Audit Log on 2013 is in its default out-of-the-box setting. I confirmed nothing had changed as well with Get-AdminAuditLogConfig. Its identical to 2010.
Exchange 2013 is on the latest CU. Single server in lab - no DAG.
I am wondering if it is something with the Arbitration mailbox. The arbitration mailbox is on 2013. Or maybe even Indexing.