I think it's just a natural reaction to getting yelled at for a good deal of people. A Google search will bring up a lot of results about crying when getting yelled at. I'm not sure about the actual biological mechanism, but even if he doesn't feel overly bad about it, it might be an involuntary reaction, especially if Quinn is being a bit gruff. He'll get better once he gets used to play at the NHL level. The kid just turned 19.
Hell, when I started a job when I was 23, I could feel tears start to well up when I got yelled at about an error during my second week (which turned out to not actually be an error--Screw you, Aaron).