From my experience:
I only use targets official debit redcard (not the amex one) that's linked to my bank account.
It automatically deducts %5 by checkout in store and online, and gives free shipping.
The catch is, that online, if I pay for a portion of the total with target gift cards, and pay the remaining portion (whatever it may be) with the redcard, it will deduct %5 from the entire order.
In store however, it only deducts %5 from the portion paid by the redcard.