Neem oil is considered an organic "dormant" oil that is applied to trees in the winter to kill insect eggs and mites. It also has some anti-fungal properties. It is a "dormant" oil in that it is to be used when a tree is bare (deciduous) or dormant, because the oil may harm young leaf growth.
Personally, I am always battling leaf miners on my adult citrus trees. I have to time treatment... dormant oil in the fall/winter every month, pyrethrins in the spring / early summer whenever the trees are showing new growth. If you have a heavily infested plant, you can remove the infested branches, and then spray dormant oil on the tree until it pushes new growth, after which you need to switch to an organic insecticide (or any type of insecticide, but I always use organics on any fruit tree I will be eating fruit off of). It kind of goes without saying, but if you have leaf-miners, you can kill the eggs or the adults, but you can't kill the larvae (since they are in the interior of the leaf eating it up).
The good news is that these critters do not touch adult foliage, so if you can treat in the winter and the spring, you are good to go over the summer once the new growth hardens off.
By the way once the leaves curl they will always look like that - it is permanent damage. So if you don't like the way they look you need to remove the leaves and hope the tree rebuds, or else remove the branch. Make sure you spray with dormant oil any time you are about to cause new budding or young growth!
