There is nothing in the New Testament text that implies that Cornelius was saved before he was baptized. I do realize that he received the give of the Holy Spirit and was able to speak in tongues, but the Bible makes it clear that this was in order to show those of Jewish descent that were with them that God could indeed work through Gentiles as well as Jews. Just as the reception of the Holy Spirit by the apostles on Pentecost showed the Jews that God was working through them. The ones there with Peter realized that Cornelius and his family were welcome by God, and agreed they should be baptized, and Peter commanded them to do so.
If the Jews were commanded to be baptized for the remission of their sins at Pentecost (Acts 2:38), and God is not respecter of persons (Acts 10:34), then baptism for Cornelius and his family was also for the remission of sins when it was commanded by Peter (Acts 10:48).
Water baptism came after he was saved.
Water baptism is a sign one is saved and has nothing to do with New Testament salvation as stated by Peter himself (1Pet.3:21), who states water baptism is a figure of salvation.