Unfortunately, you can't get have Eevee as the Hero Pokemon (the Pokemon you play as) in PMD: Explorers of Time. You can only get Eevee in Explorers of Sky if you're trying to be Eevee in the Explorers of Time/Darkness/Sky games.
Source
(You can also use that link to see what other Pokemon Mystery Dungeon games you can get Eevee as the Hero Pokemon if you have other PMD games you want to play as Eevee for the Hero Pokemon)
