Okay, it's all still a little confusing
ALL airlines are considered "participating" for ARRIVALS. You will (or should) get yellow DME luggage tags before your trip - assuming you've reserved at least ten days in advance. Attach one tag to each piece of checked luggage. Follow your NORMAL airport check-in procedures, go through Security, get on the plane, land in Orlando.
When you get off the plane in Orlando, you can go DIRECTLY to the DME counter and check in. You will be sent to wait for or board a bus to your resort. While you're doing this, DME employees are pulling all the luggage with the yellow tags after it's been removed from your any-airline Domestic flight. Once you board the bus and the bus driver has scanned your something (pass, card, something they give you at the counter) your luggage is put on a DME Bags Inc. truck and transported to your resort, where it's delivered to your room within a (usually) reasonable amount of time. You do NOT have to be in the room. Disney takes care of tipping Bell Services/Luggage Assistance.
For your return flight, IF you're on a participating airline, you can check in for your flight at the Airline check-in counter at your resort AND check your luggage through to your home airport. If you're not flying on a participating airline, and you've left your luggage with Bell Services because your flight leaves much later than checkout time, you can either pick up your luggage from them and carry it the fifty or so feet to the DME bus, or you can ask Bell Services to carry it for you and tip them.