Yeah grabbing a selected region in SC, when not using "red box capture mode" actually takes a full screen screenshot, and then displays that on the screen for you to do a region select, so it makes sense that it would pop the current full screen game out of full screen mode.
To avoid that you could either just do a full screen capture, telling SC to stay minimized, OR try changing the options to RED BOX capture mode when capturing regions, which might avoid the game popping out of full screen mode (not sure).