While the church accepted and already practiced the teaching that baptism was necessary for the remission of original sin, for regeneration, she's never necessarily accepted all of Augustine's reasoning on various aspects of this and other matters. To this day, the salvation of baptized infants is considered to be related to the will and actions of the family and community, just as "whole households" were said to be saved in Acts 16:31:
"They replied, "Believe in the Lord Jesus, and you will be saved--you and your household."
The faith of others stand in, as modeled by our Lord. Then the person would be expected to hold to their baptismal vows, with the onus on themselves and their faith as they reached the age of reason and proceeded to live their lives with whatever time and grace were allowed them.