You will not get separate tags...the flight info doesn't really matter. The lead person on the resort reservation will get the entire DME packet, with vouchers and luggage tags. It is up to that person to disburse the vouchers and tags to the others.
If you will have people arriving on different flights, get the luggage tags to them prior to departure. They can then tag their bags...DME will then take them to the resort.
Depending on flight arrival times, you may want to hold onto the vouchers, or hand them over to those on the other flight before leaving home. If the flights arrive close to the same time, you can arrange to meet up in the DME area, then go to the buses together.