All you need to qualify for DME is be named on the reservation for a Disney owned-and-operated resort, and be traveling to and from Orlando International Airport. It makes no difference how or through whom you booked your trip.
One of the problems of using a service like Orbitz is they're not going to know the ins and outs of the trips they sell.
Call Disney directly, explain your situation, and try to make your own DME reservations. If they don't let you, never fear. Wait until you're no further than 60 days from your trip and call DME directly at 866-599-0951. Make your DME reservation directly through them.
Hakuna matata ... no worries.