As we played for the first time, we would roll for the hunt right after step 4 (the action roll). As we were incorrectly allowing each side to resolve all of their actions before the other (instead of alternating die by die), the FP would move the fellowship and then add the die/s to the hunt box. The the SP would allocate their dies, roll for the hunt, then go on with the action resolution. If eyes were rolled the SP would just re-roll for the addition hunt dies added by the eyes, but it seems like it's supposed to happen all at once.
Does the hunt roll happen at the end of the action resolution?
So let's say FP goes first and uses a character die to move the fellowship a first time. Then in response, the SP rolls for the hunt, then plays their first action die. 3 dies later, the FP moves the fellowship again, so the SP rolls again for the hunt, this time only needing a 5 or 6.