You have to evolve it WHILE ITS STILL YOUR BUDDY to count. Man, I hate games where you have to Google how to play them, because instructions unclear.
For the Ripple In Time special research, it simply has two tasks: Walk with Eevee as your buddy for 10km, and Evolve Eevee into Espeon during the day.
It doesn’t say to evolve the Eevee you walked 10km with during the day, OR to keep it as your buddy when you evolve it..... fuck this game. Now I have to go get MORE exercise I don’t wanna.