When Barrin, Tolarian Archmage enters the battlefield, return up to one other target creature or planeswalker to its owner's hand.
At the beginning of your end step, if a permanent was put into your hand from the battlefield this turn, draw a card.
Barrin's last ability checks the entire turn, even before Barrin was on the battlefield.
If a permanent wasn't put into your hand from the battlefield before your end step begins, Barrin's ability doesn't trigger at all.
If a token is returned to your hand, it's put there before it ceases to exist.
The permanent that was returned to your hand doesn't have to still be there.
You draw only one card, no matter how many permanents were put into your hand from the battlefield during that turn.