Well it isn't revealed though I'm most certain that since Nagato was apart of the Uzumaki Clan as they have strong blood relation to Senju Genes causing them to be within him, though regardless of such Nagato merely had implants. I'm happy that my character still isn't effected by this as I don't ever plan on resetting an Uzumaki with Sharingan and will continue to claim Keitō having pirated rinnegan.
The only reason Nagato's hailing from the Senju lineage is because Mito Uzumaki married Hashirama Senju, the founder and leader of the Senju Clan. So that's pretty much the reason why Nagato's from the Senju lineage. The Uzumakis we have in the present day of the Naruto series are pretty much descendants of the Senju and Uzumaki Clan.
- Naruto, while we still don't know anything yet about his ancestors is quite possibly a descendant from the Senju Clan because of Kushina's genes.
- Tsunade is hailing from both the Senju and Uzumaki Clan as she is the granddaughter of Hashirama Senju & Mito Uzumaki. However, strange enough, she never used the "Uzumaki" as her middle name and remained loyal to the Senju Clan.
- Karin has we yet to know anything about. But I'll highly doubt Kishimoto even bothers to switch from Obito's background to Karin's all of sudden without a reason.