At the end of a successful run, a chest (or several chests) will appear that all players can loot. Dungeon Chest drops are taken from the loot table for the dungeon the players have completed.
At the start of the next Dungeon reset, a chest will appear in your Class Hall with loot that corresponds to the highest difficulty dungeon completed in the past week. This is based off highest clear, regardless of making the timer.
Class Hall Chest drops may be from any dungeon, including dungeons you have not yet unlocked (e.g. Court of Stars/The Arcway) or dungeons that do not have a M+ mode (e.g. Violet Hold).