Have you ever wondered how the unregenerate could say to Jesus on the judgment day, “Lord, Lord, did we not prophesy in your name, and cast out demons in your name, and do many mighty works in your name?” (Matthew 7:22). Could this power have been real, and from God, and yet not be a sign of new birth? I think so.
Consider the way Jonathan Edwards describes how the Holy Spirit works differently in the godly and the ungodly.
There is this difference; the Spirit of God in acting in the soul of a godly man, exerts and communicates himself there in his own proper nature. Holiness is the proper nature of the Spirit of God. The Holy Spirit operates in the minds of the godly, by uniting himself to them, and living in them, and exerting his own nature in the exercise of their faculties.
The Spirit of God may act upon a creature, and yet not in acting communicate himself. The Spirit of God may act upon inanimate creatures; as “The Spirit moved upon the face of the waters,” in the beginning of the creation [Genesis 1:2]: so the Spirit of God may act upon the minds of men, many ways, and communicate himself no more than when he acts upon an inanimate creature.
For instance, he may excite thoughts in them, may assist their natural reason and understanding, or may assist other natural principles, and this without any union with the soul, but may act, as it were, as upon an external object. But as he acts in his holy influences, and spiritual operations, he acts in a way of peculiar communication of himself; so that the subject is thence denominated “spiritual.” (from “A Divine and Supernatural Light”)
In other words, God could enable a person to heal the sick or cast out a demon in the same way God makes the wind blow or the waves be still, but without communicating any of his peculiar holiness. This is why supernatural phenomena are of secondary importance in discerning the hand of God. Christ-exalting, self-abasing holiness is primary.