I'm not sure. Could it be dirt from a dirt road (I guess you would know if that was it...lol)? I also see what looks like rust stains on the driveway. Maybe your sprinklers are hitting the tires and leaving rust stains? I've never heard of that but I'm just brainstorming here.
As to the tire shine, I use this stuff and it works great and lasts a while. It's not shiny but it's also supposed to treat the rubber. I prefer the matte/satin sheen it leaves.
It's the oils in the rubber of the tire coming out. Spray some degreaser on the tires (try not to get any on your rims) let it sit about 3-5 minutes them rinse it off. They will be back to black.