when I set the popup caption style to the default box setting, the fotomoto button is displayed.
when I set it to anything else, the fotomoto button isn't displayed anymore.
Do you have an example link? You mean default "block" style? "box" is not default, but should not affect the fotomoto button. The only thing that should affect the default Fotomoto button in the popup, is if you have disabled popup "descriptions" (for that page), because the fotomoto button is added into the description of the caption.