The Madone has direct mount brakes, the rear is under the frame behind the BB, so this adjuster also has a quick release lever that allows you to remove the tire. It's not just a standard barrel adjuster.
OK....
The Emonda had Bontrager Speed Stop direct mount brakes, but the release is in the brake caliper.
Did you contact Trek support? It might take a day but they do get back to you. I've had a few questions and they've been helpful. They might send you a replacement adjuster.