Because you don't use those hearts to evolve Eevee into Espeon - that's just Sylveon. What you need is happiness, which you can build by walking with your Pokemon in your team, giving it certain items, etc.
Once Eevee has enough happiness, it will evolve the next time it levels up. Make sure its daytime of course, or it will evolve into Umbreon instead.
Bulbapedia on Happiness (includes ways you can increase happiness)