Is there any explanation for the Rinnegan being on people?
That is due to the effect of Infinite Tsukuyomi.

Once it is cast:


  All those who fall under its gaze are trapped in the genjutsu, with the Rinnegan's design appearing in their eyes to represent its influence.


Just like when you can see the Sharingan pattern in Kyuubi's eyes when it was under Obito's control during the attack on Konoha.

Source:

Infinite Tsukuyomi