cic - Catholics initiation for children
there is no such thing, although folks in your parish may have used that “shorthand” abbreviation, which results in the confusion. The process through which adults (anyone over the age of reason, usually about age 7, for this purpose) are brought into the Catholic Church is the Rites of Christian Initiation for Adults. Those rites are adapted for children so that their preparation is suited to their age, abiltiy and needs, and is called the Children’s Catechumenate, but the process is the same.
they should have been instructed in the faith over a period of no less than a year, accompanied by sponsors who are usually the parents during the intitial phases, celebrated various preparatory rites to mark transitions through the phases of this process, and beginning in Lent have intensive preparation for the reception of the sacraments. they would then have been baptized, confirmed and receive first communion at the same time on Easter, during the Easter Vigil (or at another time if there was a real urgent reason).
They then should have continued further faith formation, going beyond the basics for at least 50 days until Pentecost, and hopefully continue religious education throughout their school years.
Now, I still don’t understand OP’s questions.
If there is a “group” in the Church who do not agree Christ gave authority to his apostles and their successors to baptized, confirm and confect the Eucharist, and the authority to determine how converts are brought into the Church, then that “group” needs to get with the program and decide just how far their dissent is going to carry them. For someone in such a “group” to deliberately raise doubts in the mind of a sincere convert, or in the mind of the parents who have brought their children to Christ as OP has, is a grave offense and I hope wherever this “group” is, that their pastor and bishop are made aware of their actions.
Please OP do not allow yourself to be led astray by Catholics in name only who question the authority of the Church over her sacraments, granted by Christ himself.
The RCIA is definitely intended for children over the age of reason, there is an entire section of the Ritual Book describing how these are adapted for their needs, called, as I say, the Children’s Catechumenate. Sounds like the priest in question needs better instruction from his bishop, but please, parents, do not let it disturb you in the least that some in the Church do not understand and accept. You have done the right thing. Be at peace.