If a spell or ability causes you to put a card into your hand without specifically using the word "draw," it's not a card drawn.

If two or more replacement effects would apply to a card-drawing event, the player drawing the card chooses the order in which to apply them.

Because Teferi's Ageless Insight is legendary, it's unlikely that one player will control two. However, if that happens, each card that player would draw after the first will result in four cards being drawn. If they control three, they draw eight cards, and so on.