>When you get there, you get a list of the Pokémon you have that are capable of evolving. The requirements are the same as in the main games so some require items in order to evolve. Select the Pokémon you wish to evolve and then it'll step into the springs. An animation will occur and your Pokémon will evolve. You can evolve multiple Pokémon at once so you don't have to go there hundreds of times. -Serebii
The bolded part is how you evolve him. But, you need to unlock a certain part of the game.
>You have to follow the story beyond the "end" credits through to get the mission featuring Manaphy. After you have done that, unlock the Marine Resort Dungeon and you will be able to evolve at the Luminous Springs.-Serebii
After you've done that, you should be able to evolve Turtwig.
Hope This Helped :D