posting as nothing else can be found relating to ECP redirects to OWA native ex2013 environments.
In Ex2013 CU5 a non-mailbox enabled admin accounts accessing EAC gets redirected to OWA (external URL) and fails.
the unexpected redirect for non-mailbox enabled accounts is actually a bug that had been introduced with Exchange 2013 CU3. (it was fixed in Ex2010 SP1)
The problem actually is that non-mailbox accounts are redirected to the OWA logon page in the AD site where the arbitration mailbox (SystemMailbox{bb558c35-97f1-4cb9-8ff7-d53741dc928c}) lives in.
This issue will be fixed in a future build15.00.1016.000 which will probably be CU7.
immediate fix - mailbox enable the admin account (breaking the majority of your security policies)