Miles, Golden Prodigy allows you to draw a card and then draw an additional card of another faction played this turn. This effect allows a player to draw a total of 4 cards (Draw 1 card + 1 card for Mechana, Void, or Lifebound). However, when using Tarik, the Trickster to copy Miles' effect, the player is allowed to draw 5 cards. Note that you're copying the effect, not the entirety of the card.
The distinction in this instance is that Tarik is a Monster and "Monster" is not considered a faction. As a result, the player is allowed to draw a card and then draw a card for each other faction played this turn. Since Tarik is a Monster, the player would also be allowed to draw a card when playing an Enlightened card, bringing the total to 5 cards.
In addition, in the rare case where the player has used Tarik to copy Miles and happens to have Monsters in his/her deck after defeating Samael the Fallen, playing a Monster would not trigger drawing a card since "Monster" is not considered a faction.