Christe, Redemptor Omnium

The following is a tranlsation of the hymn for Vespers, beginning the night of Christmas Eve and ending before the Epiphany. Translating it, I noticed that the hymn identifies two authors: Christ, the author of new life; and the Father, the author of Christ's coming.

The traditional translation by the incomparable J. M. Neale is availablehere.

Christe, redémptor ómnium, ex Patre, Patris Unice, solus ante princípium natus ineffabíliter.	O Christ, only Son of the Father, redeemer of all! We cannot describe how you were born of the Father alone before the beginning.
Tu lumen, tu splendor Patris, tu spes perénnis ómnium, inténde quas fundunt preces tui per orbem sérvuli.	You, the light; you, the Father's splendor; you, the everlasting hope of all: hear* the prayers poured forth by your servants throughout the world.
Salútis auctor, récole quod nostri quondam córporis, ex illibáta Vírgine nascéndo, formam súmpseris.	Author of new life**, consider that formerly you were born from an inviolate Virgin: you had assumed our form.
Hic præsens testátur dies, currens per anni círculum, quod solus a sede Patris mundi salus advéneris;	Throughout the cycle of the year, this day gives witness, that you came, the life** of the world, alone from the throne of the Father.
Hunc cælum, hunc mare, hunc omne quod in eis est, auctórem advéntus tui laudat exsúltans cántico.	Then heaven, then sea, then all found within, exulting in song, give praise to the author of your coming.
Nos quoque, qui sancto tuo redempti sumus sánguine, ob diem natális tui hymnum novum concínimus.	We who have been redeemed by your holy blood likewise sing a new hymn of the day of your birth.
Iesu, tibi sit glória, qui natus es de Vírgine, cum Patre et almo Spíritu, in sempitérna sæcula. Amen.	Glory to you, Jesus, who were born from the Virgin; glory to the Father and to the blessed Spirit, into eternal ages. Amen.

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*intende: I translated this as "hear", but the meaning contains more subtlety. This is distinct from the Latin word attende, for example, which also means "hear", and is also used in chant. I don't quite know the difference.

**Salus/salutis can refer to salvation, and this is the meaning, but the nominative salus means "health", or "vigor". It can mean "deliverance" or "salvation", but that translation seems rather narrow to me, closer to the word salvatio. Neale, of course, uses "salvation".