Yes, the support rest against the chin, but instinctively the chin/lower jaw will push forward to maintain the “normal” set up. It´s important to not relax and let it go backwards. Keep the upper and lower teeth in line, but apart of course.
Previously I had terrible problems with too much pressure on my top lip. I have built a similar device as the Stratos. When I adjust the “Stratos” support so that I hardly reach the mouthpiece, I have to force my lips to take the “muu” position. After 5-10 minutes in this position, playing relaxed with “muu”, my lips are used to make tones without extensive pressure. After this warm up, I switch to the normal playing mode without the Stratos type device. I experience that I reach slightly higher notes,and clearer tone without pressure on the lips. This new feeling stays for a shorter period during the first period of Stratos use. After a while (days – weeks…) the better position and sound stays for longer and longer time. I’m not fully experienced yet, but I feel that this recipe works for me.