The way in which Lord Viṣṇu kills the demons and protects the faithful is mentioned in Bhagavad-gītā (4.8) :

paritrāṇāya sādhūnāṁ vināśāya ca duṣkṛtām dharma-saṁsthāpanārthāya sambhavāmi yuge yuge

“In order to deliver the pious and to annihilate the miscreants, as well as to reestablish the principles of religion, I Myself appear, millennium after millennium.”

In two hands Lord Viṣṇu always carries a club and a cakra to kill demons, and in His other two hands He holds a conchshell and a lotus to give protection to His devotees. When His incarnation is present on this planet or in this universe, the Lord kills the demons and protects His devotees simultaneously. Sometimes Lord Viṣṇu appears in His person as Lord Kṛṣṇa or Lord Rāma. All of these appearances are mentioned in the śāstras. Sometimes He appears as a śaktyāveśa-avatāra like Lord Buddha. As explained before, these śaktyāveśa-avatāras are incarnations of Viṣṇu’s power invested in a living entity. Living entities are also part and parcel of Lord Viṣṇu, but they are not as powerful; therefore when a living entity descends as an incarnation of Viṣṇu, he is especially empowered by the Lord.

When King Pṛthu is described as an incarnation of Lord Viṣṇu, it should be understood that he is a śaktyāveśa-avatāra, part and parcel of Lord Viṣṇu, and is specifically empowered by Him. Any living being acting as the incarnation of Lord Viṣṇu is thus empowered by Lord Viṣṇu to preach the bhakti cult. Such a person can act like Lord Viṣṇu and defeat demons by arguments and preach the bhakti cult exactly according to the principles of śāstra. As indicated in Bhagavad-gītā, whenever we find someone extraordinary preaching the bhakti cult, we should know that he is especially empowered by Lord Viṣṇu, or Lord Kṛṣṇa. As confirmed in Caitanya-caritāmṛta ( Antya 7.11) , kṛṣṇa-śakti vinā nahe tāra pravartana: one cannot explain the glories of the holy name of the Lord without being specifically empowered by Him. If one criticizes or finds fault with such an empowered personality, one is to be considered an offender against Lord Viṣṇu and is punishable. Even though such offenders may dress as Vaiṣṇavas with false tilaka and mālā, they are never forgiven by the Lord if they offend a pure Vaiṣṇava. There are many instances of this in the śāstras.