Overview
The story of Ramayana as per Srividya ramayanam is as follows.
This starts with the conversation between Agastya and Hayagreeva. Agastya asks Hayagreeva to explain him the Guhya thathvam (secret philosophy) of Brahmmanda purana. Hayagreeva explains it to Agastya as follows.
Once Indra wanted to test the lovely couple (Agalya - Gauthama). So Indra disguised himself as a rooster and went to Gauthama's ashram before the day dawned. By making sound like a rooster, Indra tricked Gauthama and the latter went out to the river bank for having bath thinking that the day had dawned. At the ashram Agalya was left alone. Indra appeared as Gauthama and tried to misbehave with Agalya. Agalya being a pathi vrathai (one who never thinks of a man other than her husband) and a Devi bhakthai (devotee), found out the intention that Indra was having in his mind and prayed to Devi to save her and make Indra realise his mistake.
Initially before starting for execution of this task, Indra (also a devi devotee) prayed to Devi to protect him in case of any trouble. So after listening to Agalya's plea to save her, Devi turned Agalya into a stone. Now neither Indra nor Agalya would get a bad name.
Indra realised his mistake on seeing Agalya turning into a stone. Gauthama on seeing Indra at his ashram and agalya turned into a stone, judged what could have happened with the prowess of his tapas (meditation).
Read more about this topic: Sree Vidya Ramayanam