I watched this scene over and over, looking for "tells," but there was nothing obvious. (For example, one of the Reeses refers to the other has "he," rather than "it," which might be more appropriate; but the one who uses "he" is actually the real one.)
The Reese that she eventually shoots is the first one to arrive, and she shoots it right after it tells her to the shoot the other. However, neither of these would be dispositive as to whether it was real. So I think she just went with a hunch. The fact that she only shot it in the foot strongly suggests that she was not that confident that she was making the right decision; the real Reese could survive a shot off toe, if her hunch was in error.