Honey is the same as white sugar to the body. Doesn't matter that it's natural. Yes, it does have some nutrients which is great for people who are not acne prone but if you get acne then you have to keep your internal sugar levels more balanced or lower than the general population. In other words eat like as if you are diabetic. Some derms think that adult acne is like diabetes of the skin.
You must avoid all sugars (brown sugar, white sugar, honey, molasses, etc). You can eat whole fruit but not fruit juices which are too concentrated --- hence too much sugar.
The honey/apple cider treatment may work for very very mild acne but cystic acne is different...deeper. Cystic acne requires avoiding all sugars, dairy, caffeine, and anything you may be allergic to.