There are 2 different systems. When you make your resort and/or package reservation with CRO, they can also make the DME reservation for you. After that, it's done, and you'd never really need to do anything else.
But sometimes, flight information is missing. So some people are inclined to call DME directly, 866-599-0951. Problem is, DME does not have access to your DME reservation until 60 days prior to your arrival. If you call DME 61 days prior to your arrival, they won't even be able to find you in their system (which can tend to cause panic -- been there and done that, that's how I now have this info to share

).
So like I've been saying for a while, if you're more than 60 days out, deal with CRO. 60 days or less, call DME directly.
And whatever CM said that someone should wait until 13 days before arrival to make a DME reservation was clearly DEAD WRONG. You don't want to wait that long. You CAN wait that long, but there's absolutely no reason for it.