You almost never leave the paint to chase a screening guy heading way out to the corner. The idea is that the screen is likely feeding a cutting player or a penetrating dribble. You are where the play is happening. You don't run away from that spot to where nothing is happening at the moment. You take maybe a step or two in his direction after your defense has readjusted to switches caused by the screen. Any pass to the corner is going to take a second to get there. By that time you should be able to run out and cover...if you're paying attention. It's like the intricacies of knowing when you should go from 2nd to 3rd on a ground ball to the right side of infield.
If you watch McConnell, he isn't locking a guy down for 30 seconds. He only plays ball denial D for the last 8 seconds of the shot clock. He will typically be clogging a passing lane when his man doesn't have the ball for the early part of the shot clock. He has a great sense of time and space and how much ground he can cover. When he's on a very hot shooter, then he commits to full man-to-man mode and then the offensive player might as well sit in the stands because he is just watching the game.