Maya Sita or Chhaya sita does not appear in the Valmiki Ramayana. In the original Valmiki Ramayana, Ravana kidnapped Sita but not a shadow. The maya sita comes from Skanda Purana. In Venkatachala Mahatmya of Vaishnava Kanda, Vishnu describes the events happened in the Treta Yuga. He says that it was Vedavati not Janaki who was abducted by Sita. From Venkatachala Mahatmya chapter 5,
19-23 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.
24-26. Afterwards when Rãvana was killed, she entered fire once again. Agni handed over Lakshmi, my Jãnakl, who had been kept in her protective custody by Sváhá and told me about the attendant accompanying Sita: “O Lord, this is Vedavati who did what was pleasing to Sita. For the sake of Siti she rem
ained in the abode of the Râkasa as one imprisoned by him.
Hence, delight her with a good boon along with Sri.”
In the Valmiki Ramayana, there is no mention of Agni exchanging Sita with Vedavati. There is only returning after Ravana was killed.