For affairs of the material creation, Lord Mahā-Viṣṇu, the plenary portion of Kṛṣṇa, is in charge. Thus, when the Lord descends, the incarnation emanates from Viṣṇu. Mahā-Viṣṇu is the original cause of the material creation, and from Him Garbhodakaśāyī Viṣṇu expands, and then Kṣīrodakaśāyī Viṣṇu. Generally, all the incarnations appearing within this material universe are plenary expansions from Kṣīrodakaśāyī Viṣṇu. Therefore, the business of minimizing the overload of sinful activities on this earth does not belong to the Supreme Personality of Godhead, Kṛṣṇa Himself. But when Kṛṣṇa appears, all the Viṣṇu expansions join with Him. Kṛṣṇa's different expansions—namely Nārāyaṇa, the quadruple expansion of Vāsudeva, Saṅkarṣaṇa, Pradyumna and Aniruddha, as well as partial plenary expansions like Matsya, the incarnation of a fish, and the yuga-avatāras (incarnations for the millennium) and the manvantara-avatāras (incarnations associated with the reigns of the Manus)—all combine together and appear with the body of Kṛṣṇa, the Supreme Personality of Godhead. Kṛṣṇa is the complete whole, and thus all plenary expansions and incarnations always live with Him.
Therefore when Kṛṣṇa appeared, Lord Viṣṇu was with Him. Kṛṣṇa actually appears in order to demonstrate His Vṛndāvana pastimes and in this way attract the fortunate conditioned souls and invite them back home, back to Godhead. The killing of the demons in Vṛndāvana was carried out only by the Viṣṇu portion of Kṛṣṇa.