Hello,
Invoice : Define when the system will create the invoice number of an order if not already set (used also for stock managment).
You still have status like "cancel", "refund" or "pending" for the confirmed/invoice status.
So you still have the same issue for the order statuses. If the order receive any of these order statuses, the order is declared as "confirmed / paid" and the customer gets points.
Please re-read the Nicolas message for the explanations and remove all order statuses which are not meant to mark the order as "paid by the customer"
Regards,