How did the concept of Vedavati - Chaya (Cloned/Shadow) Sita emanate?

The concept of Agni hiding Sita and replacing with Vedavati - Chaya (Cloned/Shadow) Sita is not from Valmiki Ramayana. This story can be found in Puranas.

Ravana getting a curse from Vedavati was mentioned in the 60th Sarga of Yuddha Kanda of Ramayana.

शप्तोऽहम् वेदवत्या च यदा सा धर्षिता पुरा || ६-६०-१०
सेयम् सीता महाभागा जाता जनकनन्दिनी |

"Further, I was formerly cursed by Vedavati when she was humiliated by me. The same Vedavati is born as the highly fortunate Seetha the daughter of Janaka."

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The critical Edition of Ramayana, compiled by the Oriental Institute of Baroda (now Maharaja Sayajirao University of Baroda), does not contain the above Shloka.

It does not mean to say that the Illusionary Sita is completely absent from Ramayana.

Indrajit, in order to deviate Shri Rama and his army from the war so that he could gain extra-ordinary energy by performing a dangerous ritual - to eliminate Shri Rama and his entire vanara army, kills an Illusionary Sita in front of Shri Hanuman and others.

Hence, whoever incorporated the Vedavati - Chaya (Cloned/Shadow) Sita story might have adopted the concept of Illusionary Sita from the above episode.

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The following is from Skanda Purana.

Vishnu himself narrates the story of Vedavati in the Venkatachala Mahatmya of the Skanda Purana:

Formerly, in the auspicious Treta Yuga, I killed Ravana. At that time the girl Vedavati rendered assistance to Sri (Sita). Lakshmi appeared in the land of Janaka in the form of Sita. In the Panchavati forest, when I went away to kill Maricha, my younger brother followed me on being urged by Sita. In the meantime the king of Rakshasas came there to abduct Sita.

Fire-god present in the (place of) Agnihotra sacrifice knew (i.e. anticipated) the attempt of Ravana. He took the real Sita to Patala and entrusted her to (his wife) Svaha. There was a splendid lady named Vedavati. Formerly, she was touched by the same Rakshasa (but not molested). Yet she cast off her body in fire. In order to kill Ravana she was created once again.

It was she who was abducted by Ravana and kept in custody in Lanka. Afterwards when Ravana was killed, she entered fire once again. Agni handed over Lakshmi, my Janaki, who had been kept in protective custody by Svaha and told me about the attendant accompanying Sita.

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Now, a question may arise, as to the purpose for which this story of Vedavati - Chaya (Cloned/Shadow) Sita was included in the Puranas.

My understanding is as follows;

1. Elevating Shri Rama’s status as the incarnation of Vishnu and his Omniscience

In Valmiki’s version, Shri Rama was portrayed as an ordinary human, often grappling with intense emotional suffering and, at times, acting unaware of the full scope of future events.

Later commentators, focusing on devotion (bhakti), preferred to portray Shri Rama as the incarnation of Vishnu, omniscient being. In the interpolated episode of Sita’s Agnipravesha, Shri Rama was eulogised by Brahma and others as the incarnation of Vishnu and Sita as Lakshmi.

The Chaya Sita, or "Maya Sita," story portrays Shri Rama as knowing of the impending abduction and orchestrating a "leela" (divine play) with Agni (the Fire God) to create a duplicate to undergo the ordeal.

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2. Feeling blasphemous when Ravana touches Sita

For the ardent devotees of Sita and Shri Rama, Sita is considered to be Lakshmi, the eternal consort of Vishnu.

In the Valmiki Ramayana, it was described that Ravana abducted Sita, by lifting her up with his left hand at her plait of hair at nape, and with his right hand at her thighs.

वामेन सीताम् पद्माक्षीम् मूर्धजेषु करेण सः |
ऊर्वोः तु दक्षिणेन एव परिजग्राह पाणिना || ३-४९-१७

He that Ravana grabbed the lotus-eyed Seetha on lifting her up with his left hand at her plait of hair at nape, and with his right hand at her thighs.

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Devotees/Commentators might have felt it was blasphemous for Ravana to touch or kidnap Lakshmi. Hence, the Illusionary/Chaya Sita might have been incorporated, which protects Sita’s dignity by ensuring only an illusion was held captive.

Later, in the interpolated episode of Sita’s Agnipravesha, Agni restores the original Sita to Shri Rama by taking back the Illusionary/Chaya Sita.

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3. Justifying the Agni Pariksha

The Sita’s Agni Pravesha in the original text is often questioned. With the Chaya Sita concept, the fire test becomes the mechanism by which the shadow Sita is destroyed and the real Sita is returned from Agni’s protection, solving the narrative, ethical conflict of why a pure Sita had to undergo a trial.