Cocktail Tree?

The new tree begins to bear small fruit. It seems to have two fruits with velvety skin, one small fruit looks like peach with fuzzy skin, and the rest look like smoother skin. I ordered this tree online a year ago, not sure if it's a cocktail tree (it's listed on the the website as dwarf Fuyu persimmon tree). This tree starts to bloom with pink and white flowers (see previous photos). Is it possible to have this type of cocktail tree???