When playing on both mobile and PC, I leveled up bandit's talent to its final level of "if your opponent has one or fewer cards in hand during your upkeep, draw a card." During my upkeep the following turns, I drew an extra card regardless of how many cards my opponent had in hand. I saw it occur with my opponent having 2,3,4,5,6 and even 7 cards in hand.

As far as I was aware it did not matter if they had gone down to one or less before the activation, I would draw an extra card each turn even if they kept a minimum of 2 cards in hand all game prior to activating its final level ability.