The website indicates it is only for the first year and as you indicated only when you redeem at least 10 cents in each visit. The way I read it, it would likely be done as a backend (discount off the charge on your card statement). This means it would stack on top of the $1 off if you did indeed redeem that much.
This is a bit difficult because you also cannot stretch accumulated rewards into separate fuel trips (if you had 20 cents to redeem, you can't break it into two transactions of 10 cents to get the 55 cents twice). So, they make it a little tricky to use if you have multiple vehicles.
https://www.krogermastercard.com/cre...ault#default_2