The Holy Spirit accomplished the conception. Jesus was conceived in Mary's womb, not just implanted there. He was "made of a woman" (Gal. 4:4).
What Paul actually says is that Adam was "a type of Him who was to come":
Romans 5:12 Therefore, just as through one man sin entered into the world, and death through sin, and so death spread to all men, because all sinned 13 for until the Law sin was in the world, but sin is not imputed when there is no law. 14 Nevertheless death reigned from Adam until Moses, even over those who had not sinned in the likeness of the offense of Adam, who is a type of Him who was to come.
15 But the free gift is not like the transgression. For if by the transgression of the one the many died, much more did the grace of God and the gift by the grace of the one Man, Jesus Christ, abound to the many. 16 The gift is not like that which came through the one who sinned; for on the one hand the judgment arose from one transgression resulting in condemnation, but on the other hand the free gift arose from many transgressions resulting in justification. 17 For if by the transgression of the one, death reigned through the one, much more those who receive the abundance of grace and of the gift of righteousness will reign in life through the One, Jesus Christ.
18 So then as through one transgression there resulted condemnation to all men, even so through one act of righteousness there resulted justification of life to all men. 19 For as through the one mans disobedience the many were made sinners, even so through the obedience of the One the many will be made righteous. 20 The Law came in so that the transgression would increase; but where sin increased, grace abounded all the more, 21 so that, as sin reigned in death, even so grace would reign through righteousness to eternal life through Jesus Christ our Lord.
He also says this:
1 Corinthians 15:21 For since by a man came death, by a man also came the resurrection of the dead. 22 For as in Adam all die, so also in Christ all will be made alive.
And this:
1 Cor. 15:42 So also is the resurrection of the dead. It is sown a perishable body, it is raised an imperishable body; 43 it is sown in dishonor, it is raised in glory; it is sown in weakness, it is raised in power; 44 it is sown a natural body, it is raised a spiritual body. If there is a natural body, there is also a spiritual body. 45 So also it is written, The first MAN, Adam, BECAME A LIVING SOUL. The last Adam became a life-giving spirit. 46 However, the spiritual is not first, but the natural; then the spiritual. 47 The first man is from the earth, earthy; the second man is from heaven. 48 As is the earthy, so also are those who are earthy; and as is the heavenly, so also are those who are heavenly. 49 Just as we have borne the image of the earthy, we will also bear the image of the heavenly.
Jesus wasn't created in the same way that Adam was, without a human mother, and the point of the "second Adam" idea is that one man, Adam, brought sin and death to humanity, and the second man, Jesus, brought grace and righteousness to save us from our sins and to give us eternal life.
