Both awnsers are each partialy correct, the first instance where Negatos rinningan appeared was when the ninja killed his parents and he freaked out and then blamo, leaf ninja are dead and Negato was like wth???, and then again when he was with his friends and dog and was active since.
Ok so earlier I proposed the theory that you can get a rough estimate to how far the 1st hokage Harishima Senju/ the Uzumaki and their child , and Madara are away from the Sage in terms of generations. And you can use relative age of given charaters like Kakazu whos like 86ish years old was around to try and take out 1st hokage and survived using forbiden juitsu. To kind of gague how long it could have been between the Time of the sage and the time of the first hokage. Again its kind of a stretchy theory, but its not wildly crazy.
in the manga were given a family tree of the with diffrent tiers
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in the picture there are between 3-5 tiers depending on what part your looking at. and if each tier is represanative of a generation you can get about how far they are removed from the sage.
The anime version of what im talking about is but i think this one puts a more accurate version of the family tree having about 13 tiers in total
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starting at 4:40/11:33
So between the two i think its ok to say that the Uzumaki relation to the senju and the the sage of the six paths is either4-6 generations from t the family tree in the manga. And I'd say about 12-14 generations removed from the fanily tree in the anime that was just released.
Its kind of a jump from one to the other, but I'd go with the anime version this time. Because the poliferation of genetics would make more sense with the more generations and time that passes, and makes it easier to see how Negato could be of the Uzumaki clan and born/lived in the Rain have the Sages chakra and will ect and not have the last Name Uzumaki.