Yup FDF only works at the missile target location rather than actually the PD ship location. FDF only activates in the increment that the missile will intercept it's target. So if you have a PD ship set on FDF and the ship being targeted by the missile moves even 10k away it will be classed as a different location, thus when that "final" moment before impact takes place the PD will now be in a different location and thus FDF will not activate.
Area point defence will fire at any missile that is in range of both the weapon/fire control of the ship/hardpoint running the area PD mode, but any heavy PD ship running FDF is only ever effective if it piggy packs along with the ships you want defended, ideally in the same TG to prevent unpleasant mistakes as I exampled above.