Basically title, this symbol is on the tires of my new (to me) CAAD12. Are the tires on backwards? The right side of the picture is the front of the bike, the left side is the rear. This is the front tire. Another picture below showing which way the tread is facing. The tread "looks" right, it appears it would channel water away from the center correctly.
No body really confidently said. Yes, the direction matters, the arrow should point in the forward direction, if situated at the top of the tire. If there is a front/rear labeling, their respective arrows differ based on being mounted on the front or rear wheel.
That said, if you're not an avid cyclist, you'll likely not notice incorrect mounting. I wanted to find a lil something to help me better explain, but this post goes into pretty much all major aspects of tire direction all by itself. Here on MTBR
Great thread, thank you that makes a lot of sense. If I were more motivated I might do the test they mentioned but I honestly doubt I'd see much difference on a 25c tire rather than a fat MTB tire. My guess then is that the reversed front deals with turning better than the other way around and that the "tread" is basically cosmetic.