Both tires are mounted in the correct direction. The front tire is a driven tire, the angled groves should push water and gravel to the outside of the tire if it ever begins to slide during steering or braking. The rear tire is a driving tire, the angled groves should push water to the outside of the tire if it ever begins to spin under power.
If you ride at highway speeds a lot you may want to get the tires balanced sometime, but a big single cylinder engine in a light bike might produce enough vibration that the tires don't matter.
Keep us posted on what you do with the Shadow 500.