Surprisingly, I haven't seen this exact question posted anywhere on here or elsewhere (Reddit), so I just I just want to get clarification.
You have a die that shows 1, 2, or 3 shields, Qui-Gon Jin has a shield already. You resolve the die, using the ability, it does 1 damage always (and he gains shields if he can for 2 or greater die sides)
You use a card that generates shields (take cover, caution, defensive stance) and Qui-Gon Jin has a shield already. You use the ability, it does 1 damage always (and he gains the shields if he can for effects that grant 2 or more).