Elaborating on the trinity during baptism

It is a common practice in my Swiss Reformed friend’s church to elaborate on the persons of the trinity during baptism, and he was baptized that way.
This is the baptismal formula that was used during his baptism:
I baptize you in the name of the Father, A seed that he sowed in your heart. I baptize you in the name of the son Jesus Christ, your friend that sacrificed his life out of love. I baptize you in the name of the holy spirit, your lifepower that lets love grow in you.
He wants to know if he should ask for a conditional rebaptism because he finds this practice questionable.