Thanks for trying this out and sharing what you learned. So to summarize, it looks like in a household, points redeemed are deducted proportionally, but points earned are all credited to the individual member whose card is scanned. Maybe not the most fair way, but it's not hard to think this is how it's supposed to work.
Otoh, my guess is still that the offers part of the system isn't functioning like it's supposed to, but even if this is true, at least we know how it is functioning atm.