In my universe, if you time travel you become part of that timeline... sort of. It's like the timeline changes to allow for your existence? That's why I remember having Mikado as a cousin all my life even though he time traveled to my time when I was fourteen.

But also... if you change the timeline too much, it completely wipes out the future you came from. So by meeting Mikado and realizing who he really was, his future became an impossibility. Misane-chan was able to make it back to her time and things had changed, but he disappeared sometime after they entered the time machine to return again.