The little white dots are from the spider mites where they have sucked out of a vein on the underside of the leaf. You found them quick, usually, I see the spots first.

No, it is not the Neem, tho you look like maybe you have a few light burns from a missed droplet of water.

The Neem will not kill the adult spider mites. It does prevent the hatchlings from eating and thus kills them off. I forget the life span of a mite, but only a few days, I think.