I have the exact same problem with Surface Pro 4. Unfortunately, I cannot use SC (v4.12.0) at all.
Windows 10 (v1511), 64bit, Intel HD Graphics 520, latest drivers (184.108.40.20626).
Screen 1 is the built in, at native 2736x1824. Windows is set by default to display everything enlarged 200% (otherwise, everything is too small)
Screen 2, external, at native 1920x1080. Display size: 100%.
When trying to capture a region, the screen zoom 200% on the built-in monitor (i.e. 400% of original image). The same zooming carries to the external monitor.
Looking forward for a solution!