Let us say, it depends who picked the persimmon from my tree.
But as soon as the color is even orange through the whole fruit skin, they should be good to eat while firm. To achieve the full sweetness, keep them on the tree until a little bit soft or deeper orange. But it depends on your preference. My wife loves it when it is just a little sweet, so she picks it as soon as the color is uniform orange. I myself let it keep on the tree until all leaves fall (your leaf fall may be a lot later when the persimmons turns to mush due to tropic conditions), and then I pluck it and eat fresh, along with sipping a dry persimmon wine.