He has been quoted several times in articles about wanting his team to take more 3's. How many open 3 looks has Trey passed up so far? He also has been quoted several times about wanting a faster paced team, so why would he tell a player to pass up an open look? Why would he let Burke shoot a lot of 3 pointers in pre-season, have him do well with those shots, then say "Nah, stop shooting those Trey"? He isn't. True, I can not know exactly what Quin says to his team, but I can infer from what he has stated publicly about his desires for the team.
The defensive pressure from teams just picks up and he hasn't gotten good looks yet. He may be cautioning Trey not to take bad 3 point looks if the shot clock is winding down, and urging him to attack more when "ice" is called instead of wasting dribbles outside the 3pt line, which have resulted in less pressure shots.
Burke isn't on a short leash. They cut the 3rd string PG. He is going to be getting minutes all season. I'm sure there is a lot of pressure on him (put on himself individually) because this year is essentially a competition to be the backup next year between him and Neto.