How does resilient key progression work?

I’ve got the resilient 12 key and just finished timing everything on 13. My personal key is at a 12 still, I timed my final 13 from someone else’s. I didn’t get a new quest from the panda at the end of the dungeon or in dorn. Do I need to raise my personal key to a 13 before unlocking the new quest? Will my key just become resilient 13 automatically once I raise it? Obviously I could just go find out, but I haven’t found any info on this and maybe this post will be helpful to others too.