In your photo, Sirius is indeed to the right and Aldebara to the left (in Taurus). The image is how it is seen in the southern hemisphere. The drawing of the Orion constellation is not as you depict. As an example, Rigel in arabic means foot. basically, in your image, Orion the hunter should be upside down, facing Taurus with its bow/shield.
No wonder I couldn't figure out how that image was distorted. The whole thing looked wrong.