You should be fine. The odd thing is that DME generally sends out their info packets 4 weeks prior to travel....so it's too bad that your travel agency didn't get the info sent in on a timely basis. But, if they say the documents should come to you, then I guess you'll have to believe them.
I would bring anything that showed you have DME reserved with you, to the DME counter, just in case. No, you don't have to have the vouchers in hand. But you do have to have a prior reservation in their system. With no vouchers in hand, you will have to show ID proving you are the guest listed on the reservation. Not sure how they will handle that with the number of people you are traveling with though.
But, be sure to bring ID with you if you don't get the vouchers in time.
Actually? At this point in time, I would be very tempted to call DME and make sure they have you listed in their system. At least that way, you can sleep at night!!! One less thing to worry about.