I don't know enough to tell you about the recipe you found. I used the one in The Ball Complete Book of Home Preserving. It's too long to copy here. I made it but haven't used it yet, so can't tell you how it tastes. It uses cinnamon, too, which is always good, in my opinion. It's made shelf stable by the amount of sugar in it. The Ball recipe calls for 2-1/2 lbs of kumquats and 6 cups of granulated sugar, which is quite a bit more than the one you found.

The canning makes is shelf stable.

I was hoping the canning would make it shelf stable, but the recipe author says to refrigerate it after canning. Very confusing.

Canning will make it shelf stable and I see no problem with that recipe.

The only instruction I see for refrigeration is overnight before reheating and processing. That's to allow the kumquats to absorb and equalize weight with the syrup so they're less likely to float.

Of course, once a jar is opened they'd have to be refrigerated.

Carol