Type 1:
If the rescuing hero(es) has the capability to rescue a soul held in that site at the time mentioned ("at the start" means "after all heroes have entered battle and their abilities complete"), it is a rescue attempt at that site.
Type 2 and Rescuer's Choice generally:
If that soul is chosen as the soul that can be rescued, and the hero(es) has access (as above), and that soul is held in the site with the ability.