Agreed. Either coincidental coolant low, coincidental but something else, or they damaged the undercarriage. Hopefully it's the former. You don't have to take out to the dealership to check coolant level. Just look under the hood.
If the tire place damaged the battery, it's going to be interesting. When I changed my volt tires, I didn't trust the tire place to lift the volt correctly, so I actually bought new wheels and tires from Tire Rack, then took my OEMs into the tire shop to get snow tires installed. Whenever I have a tire repair, now I have enough to be able to pull all the rims off and bring them in for them to change. The locally owned place I go to is great at mounting tires (in and out in 10-15 minutes because they work like a pit crew (2 tire machines, one balancer, multiple people working on your set like a well tuned orchestra). It's amazing when I go to other national places like NTB. Firestone, Goodyear, they have a 2-3 hour wait, each one mechanic per car, bottom line, I trust them with my tires, not with lifting the volt correctly. They usually put a big jack under the rear differential on RWD vehicles and lift the entire rear end with one jack. Hopefully your tire place used the two spots under the rear springs and not the T portion of the battery.