Your theory is entirely messed up. Furthermore, I don't know why you quoted ''[Spoilers]'' on the title, as this is a mere theory and not a spoiler.
Hashirama died sometime before Shinobi World War 1 - this was proved. Hiruzen had been announced a Hokage by Tobirama during the war, meaning Hashirama died ages ago and Tobirama died shortly before the announcement. Madara lived all the way to the end of Shinobi World War 3. Your timeline is entirely wrong.
Madara awakened the Rinnegan in his old age because, he had to go through an adaptation process which Sasuke didn't need to go through. Ashura's Chakra he took from Hashirama was merely a sample of Hashirama's own Chakra, which is even lesser sample than Ashura's own Chakra, because Ashura's original Chakra quantity and quality had been decreasing throughout the times as he reincarnated to different individuals. Until it had reached to Madara's and Hashirama's era, it got so small and weak that it took Madara more than 50 years to increase with Indra's/Madara's own Chakra, which finally became the same original Chakra of Indra and Ashura that they inherited from their father's during birth and that resulted to become Hagoromo's Chakra resulting the Rinnegan awakening.
Sasuke and Naruto didn't go through this process because there was no adaptation as Hagoromo himself was already there.