Even a believer in Jesus who has repented of their sins is dead spiritually until they are baptized in water for the forgiveness of their sins (Ac 2:38; 8:35-38). Just like the water washed away all the wickedness on earth, water baptism washes away one's sins and thus saves them from their sins (1Pet 3:20-21; Ac 22:16; cf. Mk 16:15-16). When one is born of water and the Spirit (i.e. is immersed/baptized), that's when their new life as a Christian begins (Jn 3:5; Rom 6:3-4).
HS baptism was only used with the apostles and Cornelius and his family (for the combined purpose of showing the Jews that the Gentiles were on an equal footing with them; Ac 11:15-18). Its purpose had nothing to do with sin or salvation. That's why Peter commanded Cornelius to be baptized with water (Ac 10:47-48). That was the baptism that saved them.
HS baptism served its purpose in the very early church and was no longer needed. That's why Paul says there is only ONE baptism (Eph 4:5). That one baptism is so important that if a believer has been baptized, but it was not with that one baptism, the person has to be rebaptized properly (Ac 19:1-5; Mt 28:19). When one properly preaches the gospel of Jesus, those who respond to it cannot get water baptized fast enough, there is no delay. They immediately obey the command to be baptized because they want to be saved.
People who claim they have been baptized with/by the HS are just making stuff up. And if they haven't baptized in the name of Jesus (or in the name of the Father, Son, HS) for the forgiveness of their sins, they are not saved. Also, if they are falsely preaching that one must be baptized with the HS to be saved, that's a different gospel, and the consequences of doing that are worse than horrific (Gal 1:6-9).