This is funny. I just installed Mudingbuck's old, my new, QAD hdx on my Hoyt Maxxis. I used to have the Hunter Model, which it looks like you also have. I had the same problem your having with that rest and my bow shop convinced me to switch to a Code Red. I liked the CR but did not like that it dropped on a slow let down. I had the Hunter on an older bow and had no problem with fletching contact. Thats why I bought the HDX. Before installing it myself I researched set up issues.
It is possible that your rest is making contact due to bounce. The more expensive QADs all have a lock down feature. Yours does not. I think it's unlikely but possible.
During my internet search for QAD problems the most common issue I found was where people had the rest cord attached to the down cable. It needs to be mounted low, like at the bottom of the grip. When the shop mounted my old hunter they had it way to high.
Other then that you need to be sure that the two lines on the rest are lining up and that the rest is not moving to put these lines together until the last inch of your draw. It is best to be sure that your just getting the lines together with the least amount of pressure on the cable. To much pressure on the cable can throw your cams out of time and cause nock travel issues that could be driving the back of your arrow down into the rest.
Also your nock point could be off sending the back of your arrow down into the rest.
After I set up my rest I covered the fletching with lipstick to check for contact. No problems.
