Answered your own question. You did Byakko an extra 71 times and apparently your friend did Sophia an extra 301 times. The thing is, they want this content to last a bit so they delay the turn in. Do I think you should have to do 99 runs for a mount? Nah.
But SE's goal is to keep people playing it and delaying the totem turn in serves that purpose just like the mount being there in the first place. Sure, you could just do 99 anyway and stop, but I'm sure there are people out there that don't want to wait and will keep chugging along.