From what I understand, Indra and Ashura were transmigrated into Madara and Hashirama respectively during their lifetime. After both Madara and Hashirama died, their souls/chakra started looking for other hosts. We can say so because of what the Sage said,
Now that Indra's transmigration is over...
Now that the new hosts are Sasuke and Naruto respectively, Indra need not be present in Madara (since he has come back to life). Madara had already attained the chakra of The Sage of the Six Paths before he died, and since he was brought back to life using the Edo Tensei, he retained the chakra of The Sage of the Six Paths.
Also from the other things that were said in the chapter,
It is safe to consider that the souls of Indra and Ashura were not controlling the host, rather used it as a container and helping the host. So we can say that both the souls of the host and Indra/Ashura existed in the same body. After the death of the host, the soul/chakra of Indra/Ashura moved on to find another host.
Now that Madara is back to life, he has his own soul in him and lacks the soul of Indra as that is present within Sasuke.
So basically, Madara's soul is his own.