Serpentine belt and pulley

This should not be related but then we need to know the cause of the overheating. It could possibly be a burst coolant hose which is separate matter. You need to located the cause before a conclusion can be derived.

That sounds like it could be a few possiblitites, but here is my opinion.
If the car ran for a year without issue, the likely hood that the sprocket or gear was installed wrong is low as there is not many ways you can mess that up and if you did it would get the piston and valve to make contact and destroy the engine.
Timing belts last 60,000 miles on average and I don't know your mileage but I am assuming it was less than that in a year. So something made it fail. I would be more suspect of the idler wheel pulley and that the tensioner was not working right and wore the belt out. With that said I can see where the first issue got diagnosed and resolved.
When you picked it up it should have been fine but I am sure of one thing that happened and it might have been related to the bad tensioner pulley that started the whole problem. The water pump is drivent off the timing belt and the water pump pulley was probably worn and failed while driving and did so very catasprophically. Unfortunately when this happened it probably caused a situation where the vavlve and piston could make contact and damged the engine.
The water pump pulley probably had play in it and should have been checked since the belt did so much damamge. Usually the water pump gets replaced along with the timing belt. So, if this is the case it was just a bad call made on the mechanics' part. They should have replaced the pump and everytihgn else that gets replaced, usually called a timing belt kit, when a timing belt is replaced whcih as I said includes the water pump. It did fail much worse than expected and I am surprised that there was not some residual coolant leak around the pump when they fixed it since it was so close to failing.
It is one of those things that happens. No mechanic can be perfect, but they should have replaced all the items as if it were a new belt. And it was. Some will say that the practice of replacing the pump and cam seals, etc. In a kit is overkill but they do make kits that come with these parts. I think especially since of the failure it should have been done.