Ask Mr. Smarty Plants

If you will look at the photo on the Diospyros texana (Texas persimmon) species page, you will see that some of the leaves on the tree in that photo have cysts similar to those you describe.  These are called leaf galls.  One possibility for these galls is Aceria theospyri [synonym = Eriophyes theospyri] (Persimmon Leaf Blister Gall).  Here is a description from the Florida Bureau of Entomology.  Persimmon leaf blister gall isn't caused by an insect, but by a mite—a relative of ticks.   Galls are growths by the plant in reaction to the insect or mite laying an egg in its tissues or to an insect or mite feeding on the plant's tissues.  This article (Gall-Making Insects and Mites) from Texas A&M AgriLife Extension and this one (Insect and Gall Mites) from University of Minnesota Extension Service both say that galls are not usually deleterious to the plant.  They may result in early leaf fall, but, in general are not especially harmful to the plant.  They usually don't warrant any control measures such as chemical spraying.   Indeed, spraying them after the galls have formed is not effective since either the damage is done and the insect larvae is encased within the gall or the feeding process has been completed.

In answer to your specific questions, you shouldn't be especially concerned about the galls and treating them would most likely be ineffective.