Agree mostly of it,...
My theory.
So when the Sage on seeing what is happening thru Naruto, he appeared.
He said to Naruto, "Now is the right time" and also said "The things you did too".
My theory.
When the Sage divided Juubi into 9 parts, he may had put some of his chakra into the last part Kurama.
Then when Naruto win against Kurama, he gained the look-alike Sage cloak, when in bijuu mode.
Kurama was unique as he can sense (detect) evil from afar.
As "Time Traveling" Sage, he could have stay inside Naruto mind, understanding Naruto behavior and the ninja world.
Could be the same method as both Minato and Kushina appeared inside Naruto.
Minato stop Naruto at the point when Naruto wanted to pull out the seal.
Then when Naruto win against Kurama, he gained the look-alike Sage cloak, when in bijuu mode.
Kurama was unique as he can sense (detect) evil from afar.
As "Time Traveling" Sage, he could have stay inside Naruto mind, understanding Naruto behavior and the ninja world.
Could be the same method as both Minato and Kushina appeared inside Naruto.
Minato stop Naruto at the point when Naruto wanted to pull out the seal.
So when the Sage on seeing what is happening thru Naruto, he appeared.
He said to Naruto, "Now is the right time" and also said "The things you did too".