“Celebrated worthily in faith, the sacraments confer the grace that they signify. They are efficacious because in them Christ himself is at work: it is he who baptizes, he who acts in his sacraments in order to communicate the grace that each sacrament signifies. The Father always hears the prayer of his Son’s Church which, in the epiclesis of each sacrament, expresses her faith in the power of the Spirit. As fire transforms into itself everything it touches, so the Holy Spirit transforms into the divine life whatever is subjected to his power” (Catechism of the Catholic Church, 1127).
“This is the meaning of the Church’s affirmation that the sacraments act ex opere operato (literally: ‘by the very fact of the action’s being performed’), i.e., by virtue of the saving work of Christ, accomplished once for all. It follows that ‘the sacrament is not wrought by the righteousness of either the celebrant or the recipient, but by the power of God’ (St. Thomas Aquinas, STh III, 68, 8). From the moment that a sacrament is celebrated in accordance with the intention of the Church, the power of Christ and his Spirit acts in and through it, independently of the personal holiness of the minister. Nevertheless, the fruits of the sacraments also depend on the disposition of the one who receives them” (Catechism of the Catholic Church, 1128).
St. Thomas sums up the various aspects of sacramental signs: “Therefore a sacrament is a sign that commemorates what precedes it–Christ’s Passion; demonstrates what is accomplished in us through Christ’s Passion—grace; and prefigures what that Passion pledges to us—future glory” (St. Thomas Aquinas, STh III, 60, 3).
Therefore, the sacrament(s) celebrated by a priest who is on the list is/are valid and legal; there is no need to re-baptize the person or to renew the marriage vows if the sacrament was celebrated by one of these priests.