Well, there could always be a simple prompt.
"Claws reach from the afterlife as if you grab your soul..."
"Face the Oversoul Buffalo?"
Yes< No
-You are now bound by Duty-
You're taken to an instance for the Oversoul fight.
Your 10th buffalo kill could cause a (!) to appear on your minimap NEAR his usual location that you can use to initiate the duty.
For Ifrit (or other BCNMs), it's a bit easier. You would simply have to be the one who takes the party in. Check the aether:
Bowl of Embers (Hard)
Bowl of Embers (Oversoul)<