No, Ashuras chakra probably didn’t reincarnate until the Indra reincarnate died so they could both reincarnate at the similar times. It reminds me of a random theory I have that Madara getting his rinnegan. It’s that he only received the rinnegan near his death because it was around the time hashirama died, though that is debatable because hashis edo tensei was young. But like ashuras chakra went to Madara when hashi died since he had Hashi DNA, and then the chakras mixed making SOSP chakra making rinnegan. Then when Madara died.