First off, don't think of them as "whiskers". Think of them as actual marks on his face because well, that's what they are. It's like having moles/freckles. They are apart of his dna and an actual trait of his just like his blue eyes or yellow hair, so it's only natural that the marks on his face can be passed down too.
While the nine tails chakra may have given him that characteristic, they are still Naruto's genetic traits, so the passing down of them has nothing to do with Kurama really. So it's also likely that the kids don't have anything to do with Kurama either, they just got their dad's skin marks
