The extra tags for folks flying Southwest is a function of whether someone at DME physically handles your reservation and who that someone is. I last spoke with DME about a month ago - had to change reservation due to flight change necessitated by the 737-Max8 grounding. Since I had them on the phone, I requested additional tags. i was told that it was already noted on my reservation. Knowing that I had not requested it, I asked about it. He told me that most of the DME folks will automatically flag any reservation with a Southwest flight to receive 2 tags per person. The thought being that since you can have two bags free, a lot of people will decide to do that. It saves everyone time (and hence, money) to just print and send a second set of tags. Apparently, it doesn't always happen - it's not part of the "standard" process. But the agents have that ability and the more seasoned ones tend to do it as a matter of course.
Also, just for clarification, DME is NOT part of the Disney Company. It is a separate entity (owned my Mears). Their IT is not connected to Disney's in any way, other than they have read access to your Resort Reservation via your confirmation number.
If you ever have a question or issue regarding an aspect of DME, call they directly at 866 599-0951. Whatever you do, don't call Disney Reservations, as they won't be able to help you much.
Steve