Before leaving the subject of vicarious atonement, it is in place here to notice its relation to the soul of man. For, while Christ's atonement has primarily this objective relation to the Divine nature, it has also a secondary subjective relation to the nature of the guilty creature for whom it is made. The objective atonement is intended to be subjectively appropriated by the act of faith in it.
Dogmatic Theology, page 409 (emphasis in original)
Likewise, Shedd explains that
Unfallen man was a member of the heavenly family merely by the fatherhood of creation and providence; but after his rebellion and apostasy this ceased to be the case. Redemption was needed in order to restore him to membership. The whole human family are not now God's heavenly family. Only a part of it are the dear children of God. Those only are members of God's family who are members of Christ, "of whom the whole family in heaven and earth [the church above and below] is named," Eph. 3:15. All others "are bastards, and not sons," Heb. 12:8.
Dogmatic Theology, page 422 (footnote omitted)
While Shedd does say that "It does not mean that Christ's vicarious atonement naturally and necessarily saves every man ..." (Dogmatic Theology, page 437) but Shedd goes on to explain that "The atoning Mediator can demand upon principles of strict justice, the release from penalty of any sinful man in respect to whom he makes the demand."