A typical purchase looks something like this for me.
After the items have been scanned, show the Cumulus card back in the wallet. Credit card to the reader back in the wallet. Receipt in the wallet. Coupons forgotten... because I didn't see them among all the receipts.
I would find it more practical if I pay with my credit card and the points are automatically credited to my Cumulus account and any vouchers are taken into account. If I need a receipt, I can print it out later or ask for it at the checkout, like at Migrolino. So that the customer is still informed, this can be mentioned again in the statement, which would also be sufficient for me personally as a PDF in the email.