Answer from Praveen Bharghav, Wildlife First:
Only those species of animals/birds listed in the Schedule I to IV of the Wildlife (Protection) Act, 1972 are protected. Possession or trade in such species is prohibited. Wild animals including their parts are classified as “prohibited items” and cannot be imported under the Foreign Trade (Development & Regulation) Act, 1992 and the Export & Import Policy. Therefore, if the “non native” birds you are referring too are found in the wild outside India, they cannot be imported and action can be initiated under the said Act.