It should be based on where the player resides when earning the money. So, if you're on a contract to the Capitals, but playing/living in Hershey, PA you'd pay Pennsylvania taxes, not DC taxes.
But, there's also other things at play, like earning money in a state where you don't reside being subject to taxes in that state. I'm not 100% sure if the NHL contracted AHL players earn 1/68th of their salary per game, or how exactly it breaks down, but I'd think that at least some of their salary is subject to taxes in other states due to away games.