Moon passage from the movie.
I hypothesized that when the war broke out on the moon to deal with what to do with the Indra Ashura war, many defected and lived on Earth.
That's why i think that the Uzumakis came from Hamura's bloodline as well. The Hidden Eddy Village (Uzumaki Clan home) is right next to the Hidden Leaf (Hyuga, Senju, and Uchiha Clans).
The fact that the Hyugas were there when Hamura is on the moon means that there was a way to go to the moon and earth respectively. (We know this from the movie)
It's also backed up by the fact that Toneri (from the branch) had chakra mode due to tenseigan meaning its a yang thing (Hamura was the Yang and Hagoromo was the Yin).
Who knows? If the chakra cloak was an Uzumaki feat (minato couldve learned it), then they could've belonged to the branch fam.
That's my take on it.
So war broke out between houses. They fled. They resided to their distant cousins: Uchiha and Senju. Then that's the end of it. Oh yeah, Uzumaki got gangbanged by 4 villages, and its all thanks to Tobi, and Konoha was too busy sticking a finger up their bums while picking their noses than helping their ally/relatives