You can make the DME reservation yourself. Everyone listed on a Disney resort reservation (including
DVC reservations) is eligible to use DME. Not everyone on the reservation has to use it, it doesn't have be used for both ways, and it doesn't have to be used on the first and last days of the resort reservation.
The simplest thing to do is call DME directly at (866) 599-0951 and tell them what you need. Do not call Disney Reservations or any other Disney phone number - they generally won't be able to help you and are most likely to give you incorrect information.
Technically, DVC Member Services will say the member has to book the DME reservation, in the same way the member has to book any dining plan for a guest. But DME doesn't care who books it. The only information DME cares about is the resort reservation number and the flight info. (Well, they don't really care about the arrival flight either, just a rough time).
Also, if for some reason you didn't make a DME reservation, you can just show up at the DME desk and they'll look you up and get you on a bus.
Steve