Other people seemed to be ignoring them, so I'm not sure if they pop mimics or not. But I didn't get any.
The reason that other people are ignoring them is because they can't see them. Treasure chests only pop up when you are doing a leve and it is specific to you. Only the person in the leve can see, open and recieve the items/gil from a chest. If you don't open it the whatever reward is inside is lost.
As far as I can see there is no correlation between which leve you are doing and the chance of the chest. And just because you have found a chest doing a certai leve does not mean that the next time you do it you will find one. I have found chests doing Battle and Fieldcraft Leves. But I have found that the gil reward you get from the chest is higher when doing higher level leves.
Also if you are in a party doing a leve and one person opens a chest, then everyone in the party recieves the gil.