You have to find a shop atop a mountain. That shop will be selling the Evolve Gun. Buy the gun, load it with an evolution stone, aim it at Eevee, and shoot the f**king Eevee
You have to use it. I made the same mistake once but didn't notice I misclicked and thought it worked like that.
By the way, what's your favourite Eeveelution? Mine is Flareon (ブースター)