I got this targeted Offer on my new Qantas Amex Discovery card, after I made my first small $1.50 transaction at Woolies on that card.
I definitely didn't get it on my existing DJ Amex card on which I make all of my large Woolies purchases.
If someone has a new or old Amex card that they've never used at Woolies before, then it might be worth trying to make a small Woolies purchase on it, to see if the offer is triggered.
Offer terms:
Woolworths Welcome Offer
Spend $10 or more, get $5 back
Save the offer to your eligible Card and spend $10 or more, in one or more transactions, online, in-app or in-store at Woolworths by 01/12/2019 to receive one $5 credit. Limited to the first 40,000 Cards to save the offer.
Its for new customers only I think.