Correct that we do have Daily Quests in the game, but Daily Quests do not award Loot Chests on completion, they award Gold.
Leveling up a Hero in the game will always level your Player Level, because your Player Level is a sum total of your Hero Levels. Your Player Level dictates the rarity of the Loot Chest you get from leveling up a Hero. Every 5 levels that chest will be Rare, and every 25 levels that chest will be Epic.
This is how the system has worked since we introduced it with Heroes 2.0, the bug showing that you are getting 2 chests is a display bug, that is causing confusion based upon the functionality that has always existed.
We apologize for the confusion, but you are not missing any chests. Thanks for the report!
Huginncord