Are chests shared in co-op?

The catch is distance: the share only reaches players who are close enough to whoever opens the chest. If your party has split up to cover more ground, a chest opened on one side of the map does nothing for the player on the other.

Inside a Sanctum this is rarely a problem. You are moving through it together, and every party member receives the loot when a chest there is opened. Out in the open world it pays to stay grouped when you know a chest is coming up, and there is no reason to race each other to it.

The reward goes to players who have not opened that chest yet. A cooperative party holds up to four players, so one opening can pay out to all four of you at once.

Not settled: The game gives no exact distance for "close enough", so the safe habit is to stand near whoever opens the chest.