Board Thread:Naruto Discussions/@comment-30323490-20170604171211/@comment-4912646-20170606024553

All we know about Hagoromo's position in the afterlife is that he can appear in the minds of his sons' reincarnations ("depending on their power" according to Black Zetsu), he can briefly manifest in the living world (but only when Indra's, Asura's, and Kurama's chakra are combined) and he says he'll talk to Obito when he gets back to the Pure World. So it sounds like he does in fact reside in the Pure World like the rest of the deceased but can essentially come and go as he pleases (perhaps due to the power of the Outer Path going by Konan's statements).

Also interesting to note that Hagoromo talks as if he has met his sons' reincarnations several times before, but apparently Hashirama and Madara weren't among them.