If you just have a water softener then the problem is 1 of 2 things.
If you are on Well water, and the softener's timer was down for a while, your tank could have been storing all the iron, hydrogen sulfide (yes I know that's a gas, but it leaves black flecks in the tanks) , and sediment that came up from your well. When the controls were cycled, it raised the resin bed and all the build up. Once the system was cycled to the home position, that build up was still in the manifold, and loose inside the tank. When you turned your water on, that's when it started shooting into the pipes of your house.
Now if you're on municipal/city water, the second reason could be when the city was purging the lines under the street, the junk that they're trying to clean out comes into your house if you're using the water. It gets stored in your softener and once the bed is disturbed it's a constant headache for days after.
I don't know what special mix they put into your softener because resin should be the only thing put into a softener. I'd have simply put the softener in backwash, unplug it, come back an hour or two later, plug it back in, and then let it cycle itself through. I get paid by the hour though, so that might have played into why they'd rather rebed the tank.
I'd call them and ask if they put carbon in the softener with the resin because the water can come out black for a while after that. It's not recommended though. The carbon would need eventual replacement, but the Rain Soft resin comes with a lifetime guarantee and should never need replacing.