It turns out that you have found a bug. If you copy and paste a shape path to a shape path the position of the paths is identical. If you copy a shape path and paste it to a mask path on the same layer, the new path will be shifted down and to the right 1/2 pixel. Here's how I ran the test.
I started by creating a shape layer with the pen tool, turned on snapping, set up a horizontal and vertical guide, and made sure that the first vertex was exactly at comp center. Then I started copying and pasting the paths, first the shape path to a shape on the same layer, then a shape path to a mask on another layer, then a shape path to a mask on the same layer. Then I ran the Create Nulls from Paths/Trace Paths script on all of the paths and verified the position. As you can see by the screenshot the only position property for a null that is off is the mask path on the shape layer.
The fix is to set the magnification ratio to 200%, select the path in the timeline, select the selection tool (v) and double click the path to select all points or press Ctrl/Cmnd + T to free transform the path, then use the arrow keys to move up and to the left by clicking once on each arrow key. If you have an HR display (Retina), you'll have to set the Magnification Ratio to 400% to get the arrow keys to nudge a half pixel.
I ran the test on a Mac with a Retina display. I'm not sure that the same problem exists on a standard display. I'm reporting the bug.