Yes, you still need to feed your Eevee candies to evolve it. The trick you're referring to is a popular trick to control which Pokémon Eevee will evolve into.
In the traditional games, you need to give Eevee an evolution stone to make it evolve. A Water Stone for Vaporeon, a Thunder Stone for Jolteon, and a Fire Stone for Flareon. Since these stones don't exist in Pokémon Go, Eevee evolves randomly into either.
To avoid having to rely on luck, people have attempted to determine what Eevee will evolve into. Eventually, it was discovered that renaming Eevee allows players to define which Pokémon Eevee will evolve into, assuming that evolution had not been registered in their Pokédex before:
| Evolution | Eevee Nickname | Regular Evolution method |
|---|---|---|
| Vaporeon | Rainer | Chosen at random if no other evolution requirement is met |
| Jolteon | Sparky | Chosen at random if no other evolution requirement is met |
| Flareon | Pyro | Chosen at random if no other evolution requirement is met |
| Espeon | Sakura | Walk 10km with Eevee as your Buddy, and evolve in the day |
| Umbreon | Tamao | Walk 10km with Eevee as your Buddy, and evolve at night |
| Leafeon | Linnea | Evolve near Pokéstop under the effect of Mossy Lure |
| Glaceon | Rea | Evolve near Pokéstop under the effect of Glacial Lure |
| Sylveon | Kira | Earn 70 Hearts as your buddy |
Restarting the game is only used to ensure that your Eevee has been renamed, since the servers aren't always available. By restarting, you can determine if your Eevee has been successfully renamed before you spend candies to evolve it.
Of course, this doesn't change the fact that you still need to candies to evolve your Pokémon. Also keep in mind that the trick only works if you haven't registered the respective evolution in your Pokédex yetonce per nickname (thanks @MBorg).
