I recently setup an Exchange 2013 Server in an Exchange 2010 Environment.
All worked fine, but logging in to https://exchange2013/ecp redirected me to the old Exchange 2010 Interface.
If you have this problem, you can add the Exchange Version to the URL using “?ExchClientVer=15”.
So https://exchange2013/ecp?ExchClientVer=15 will redirect you to the correct Management Interface.
Sidenote: If the Mailbox of the Administrator account resides on the new Exchange 2013 Server this will be obsolete.