The puzzle text is misleading and has been fixed (haven't updated the download) The thing that tripped you up is that there's only one of each. So there has to be one explosive, one non explosive and one both. If you check the chest that says explosive you can not know if it has both or just-non explosive inside. Just to simplify let's call them A, B, and AB
Chest says A, gives B. Can either be B or AB. Chest that says B gives A, so it can either be A or AB.
You have to check chest that says AB. It gives B so it can only be B. Then the chest that says A has to be AB, and the chest that says B has to be A.