The battery light rarely (never?) indicates a problem with the battery. Instead, it indicates some sort of problem with the charging system (alternator, diodes, voltage regulator, wiring, etc.).
If the light at a fixed interval (i.e. twice per second or something), then the computer is trying to tell you something and you should probably have a mechanic check it out. Some chain stores will test a battery & charging system for free, others it is usually less than $10.
If the light is blinking "randomly" then it is possible that the parking log broke a wire underneath somewhere, and this probably won't be too hard to fix at a shop with a lift (prob an hour labor at most).
It is unlikely, but not impossible, that the shop damaged your charging system when you got your tires. Some shops will do a check on every car that comes in the shop, which usually includes a quick check of a few things under the hood- if they accidentally damaged something when they did this check then the shop would be responsible, but I can't imagine how it would have happened. I suspect the parking log thing more.
What kind of car?