Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
Nashor's Tooth -- Provided you achieve an attack speed greater than 1 you won't need any other Attack Speed item. This is partly because of Ravage which acts as an incredible attack speed multiplier.
Essentially this build takes advantage of Evelynn's E Ravage, which notably applies on hit effects for both attacks, to burst down an enemy with items like Lich Bane or Nashor's Tooth. After you have these items, your basic attacks now deal Magic Damage and you can simply buy AP items. NO MORE SPAMMY Q. jk. Because this build is considered a hybrid between AD and AP (because of Eve's auto's dealing magic damage primarily) you do not sacrifice the damage done via Hate Spike.