It could be a coincidence, no way to tell for sure, but there’s a pretty good chance the overheating is a result of the work just done. More likely to do with the water pump work than the timing belt, but it could be the timing belt too. A water pump job requires at least some of the coolant be drained; after the pump is installed the coolant needs to be refilled and then any air that has gotten into the cooling system during the job has to be bled out. I’m guessing the shop probably forgot to refill the cooling system. Don’t rely on the plastic bottle to check the fill level, when the engine is cold remove the radiator cap. It should be full of coolant right to the top of the radiator, or nearly so, within an inch. Another possibility is the water pump belt isn’t properly tensioned, or the replacement pump is faulty. Or there’s a leak.
So why didn’t it overheat right away? It takes some time for the engine to overheat when it is low on coolant. How long depends on how low the coolant level is. Good idea as posted above to make sure the radiator fan is coming on when it should. When the engine was overheating, the radiator fan should be spinning at full speed. If it isn’t, that could be the problem rather than low coolant. If so, the shop may have forgot to re-connect the coolant temp sensor that controls the radiator fan.
Remember that in overheating incidents the driver can usually effect some extra engine cooling by turning on the heater and the heater fan to max.