Your answer is not correct. I have explained the order in the previous answer. Here are the directives from the USCCB, commenting on the rubrics of the Missale Romanum.
usccb.org/prayer-and-worship/liturgical-year/triduum/roman-missal-and-the-easter-vigil.cfm
*Liturgy of Baptism
The Missale has reorganized the rubrics for this entire section of the Vigil (nos. 37-58). Nevertheless, the Rite of Christian Initiation of Adults should always be consulted in conjunction with the rubrics mentioned here in the Missale. This is especially true when Baptisms are taking place by means of immersion.
Christ’s Passover and ours are given full expression when baptismal water is blessed in the font and when the Christian initiation of adults, or, at least the baptism of infants, takes place at the Easter Vigil. Even if there are no candidates for baptism, the blessing of baptismal water should take place in parish churches. At the very least, baptism should be commemorated by the blessing of water intended for sprinkling upon the people.
The rubrics describe two instances of Baptism at the Vigil. If there is a procession to the baptistery or the font, the catechumens are called forward and presented by their godparents. If there are children, they are carried by their parents and godparents to the front of the assembly. Those who are to be baptized, along with their godparents, are led first by a minister with the Easter candle; the other ministers, deacons and priest follow after them. This procession is accompanied by the singing of the Litany of the Saints. The priest then gives the introductory statement.
If the Baptisms take place in the sanctuary, the priest makes the introductory statement and this is followed by the singing of the Litany of the Saints.
When there are no Baptisms and the font is not to be blessed, the litany is omitted and the blessing of water takes place at once (EV, nos. 39-41).
The Missale reminds the celebrant that during the blessing of the water his hands are outstretched (EV, no.44).
Numbers 48 to 53 of the rubrics for the Easter Vigil of the Missale Romanum describe the initiation process. As was mentioned before, it is important to closely consult the Rite of Christian Initiation of Adults on this matter. Number 48 of the rubrics for the Easter Vigil mentions that after the renunciation and profession of faith “if the anointing with the Oil of Catechumens did not take place beforehand, as part of the immediate preparatory rites, it takes place at this moment.” Of course no. 33 of the Rite of Christian Initiation of Adults points out: “The National Conference of Catholic Bishops approves the omission of the anointing with the oil of catechumens both in the celebration of baptism and in the optional preparation rites for Holy Saturday. Thus, anointing with the oil of catechumens is reserved for use in the period of the catechumenate and in the period of purification and enlightenment, and is not to be included in the purification rites on Holy Saturday or in the celebration of initiation at the Easter Vigil or at another time.”
Number 49 of the rubrics for the Easter Vigil notes that when there are many to be baptized, the priest may ask for the renewal of baptismal promises of all present immediately after the profession of faith made by those to be baptized, along with the godparents and parents.
The celebration of Confirmation is to take place in the sanctuary as indicated in the Pontifical or the Roman Ritual.*
Liturgy of the Eucharist
Care should be taken that, particularly in regard to this night’s celebration of the Eucharist, the liturgy is not done in haste and that all the rites and words should be given their full force.
The Missale has incorporated into itself rubrics found in nos. 241-243 of the Rite of Christian Initiation of Adults. These allow for a commemoration of the baptized and their godparents to be made in the Eucharistic Prayer. Proper formulas are found in the Roman Missal for each of the Eucharistic prayers (EV, no.63). The Rite of Christian Initiation of Adults indicates that these formulas are found in the section for ritual Masses, “Christian Initiation: Baptism.”
The Missale reminds the priest that before he says, This is the Lamb of God, he may make a brief remark to the neophytes about their first Communion and “about the preciousness of so great a mystery, which is the climax of initiation and the center of the Christian life” (EV, no. 64). In no. 65 the rubrics for the Easter Vigil indicate the desirability for the neophytes as well as all the faithful, if the diocesan Bishop consents, to receive Communion under both kinds.
The Missale provides a solemn blessing to conclude the liturgy (EV, no.69). It is used in place and can presently be found in the Sacramentary at no. 6, “Easter Vigil and Easter Sunday.” It is also possible to use the formula of the final blessing in the Order of Baptism for Children, according to circumstances.
The very last rubric reminds us that “the Easter candle is lighted in all of the more solemn liturgical celebrations in the Season of Easter” (EV, no. 70).
Thus, as I have already explained, following the Service of Light and the Liturgy of the Word, and after the homily, there follows the Baptismal Liturgy during which catechumens are baptised, candidates are received into full communion, and they are all confirmed. Following this is the Liturgy of the Eucharist and it is at the point of Communion that those who had been earlier Confirmed receive their First Communion. This is done according to the ancient order of the reception of the sacraments of initiation: Baptism, Confirmation and Eucharist.
