I have my advice set up the way you have yours as I want to know about ALL orders. I then check against the advice from PayPal. The reason is that I can follow up on orders that do not complete.
Your admin advice to receive these order details is in:-
.. admin_order_info.php
Send Notification to Administrator
I guess that, if you uncheck this and, instead, go to your Payment System and click the Final Checkout Page:
.. admin_order_final.php?payment_id=
Send Notification to Administrator
You can select to receive e-mails on 'Success'.
I hope this is right and helps with your problem