The old system evolutions using splinters and stones in Pokemon GO has been replaced by Stardust and Candy Evolution system(via chocolates). The system works similarly. Players must collect enough candy to develop pokemon before the next evolution. Players get candy when catch Pokemon previously captured. In the case with Pokémon Eevee players will have to re-capture the Pokémon until they get enough sweets for the evolution.
Members Reddi looking for clues and ways to control the process of Eevee evolution. On one of the branches of Reddit, group of users has teamed up to exchange data and to find a pattern in the evolution of Pokémon. Pokemon Go randomly decides which evolution happens as a result of the necessary conditions. And, of course, to devote even more time to only one Pokemon.
With subsequent updates will probably be clarification with regards Eevee. In the meantime, we are watching the experiment on Reddit, and will keep you informed.