Applying a balanced fertilizer w/o a soil test always carries with it the potential for creating or contributing to a toxicity of one or more nutrients. To wit, if there is an adequate amount of phosphorous and or potassium in the soil, fertilizing with a balanced fertilizer can create toxicities of either/both nutrients. When acting on advice resultant of a soil test, all nutrients essential to normal growth should be represented in the soil at favorable to ideal levels, which is (or should be) the ultimate goal of supplemental nutrition.
Bad advice is instructing someone to fertilize willy nilly with a product that has as much as or more potential to create a problem than resolve one. It's easy to poison the well by simply saying someone is providing bad advice ...... not quite as easy to be specific and point to the error.
Persimmon trees are self pollinating, which is not to say they don't benefit from cross pollination. With few exceptions, fruit will not form until pollen from male parts are transferred to the female parts of a flower. Without pollination, flowers may bloom abundantly, but will not bear fruit. If at any point a persimmon tree produces fruit, pollination has already occurred, so it is not a 'lack of pollination' that causes shedding of fruits that have already set.
Fall IS a very good time to fertilize. It helps strengthen the root system, which continues to grow after fall defoliation, increases resistance to chill (nutrients act as intracellular antifreeze), and since nutrients can be stored within the plant, fall fertilizing ensures a more robust spring push.
BTW - there is no credible evidence that fall fertilizing with products that include nitrogen (N) detracts from the plant's ability to resist chill, or that N forces tender growth destined to be killed by chill injury. Plants begin setting buds in mid to late summer; and while N does provide building blocks essential to new growth, plays no role in initiation of bud break. Bud break is regulated almost exclusively by day length (actually, it's the length of the dark period). A plant's ability to resist chill is initiated by increasing length of the dark period and sealed by increasingly cold temperatures. Cold hardiness is enhanced by regular fertilization well into the fall and early winter - as long as soil temperature remain above 55*F so soil organisms can turn ammoniacal N into nitrate forms which can be stored in the plant. In spring, when soils are cold and N difficult to access, stored N (and a full compliment of stored nutrients) play an essential roll by fueling early spring growth.
Al
