I blast them with water. Then would try neem oil water and soap mixture.

Insect pests will come to them, but generally bugs show up when plants are under stress. If they get problems, it's usually aphids, red spider mites, mealy bugs, which can be taken care of soap and water (40 parts water, 1 part liquid soap) 20 ounce spray bottle (20 ounces water, 1/2 ounce OR 1 Tbsp of liquid soap). If you have mealy bug or scale (they have waxy coatings), then add 8 parts rubbing alcohol to the 40:1 mixture, which breaks down the waxy cover of the bugs.

There are a number of sprays that will get rid of the aphids. Watch the ants and see where the worker ants are going. If they have a next in the ground . If the worker ants have a trail from the tree leading to the ant hill or next, get Orthonex (a white powder)and sprinkle powder along the trail. The worker ants will get it on their bodies and take it into the next, where it will wipe out the entire next or colony. Without the ants, you will not have aphids.

I would just let nature do it's thing. You probably separated the ants from the queen, so the problem will resolve itself

I have no idea the thought of growing a pomegranate tree is totally foreign to me.