When did the change-over take place? It could not have been in the time of Christ, since he sent his Apostles out into the world, instructing them to baptize people (which could not refer to a "baptism of the Holy Spirit" experience).
Spirit baptism
(the gift of receiving the Spirit via by the laying on of hands) is something that believers sometimes could administer under God's authority and will. To my knowledge, this is something that has happened 4 times within Scripture (even within the OT).
Occurence #1.
"And Joshua the son of Nun was full of the spirit of wisdom; for Moses had laid his hands upon him: and the children of Israel hearkened unto him, and did as the Lord commanded Moses." (Deuteronomy 34:9).
Occurence #2.
17 "Then laid they their hands on them, and they received the Holy Ghost.
18 And when Simon saw that through laying on of the apostles' hands the Holy Ghost was given, he offered them money,
19 Saying, Give me also this power, that on whomsoever I lay hands, he may receive the Holy Ghost." (Acts of the Apostles 8:17-19).
Note: Yes, I am aware that Simon was wrongfully asking for the Spirit via by offering money, but the point here is that the saints were able to be vessels to which to administer the Spirit of God by the laying on of hands; Again, this is not to say that the Spirit cannot be received in other ways like in receiving the gospel, or in being water baptized. Being water baptized is something that the Jewish apostles did and they followed in this teaching (even to baptize Gentiles) until Paul received new revelation on the matter (of which we get to see in Acts of the Apostles 19:1-6).
Occurence #3.
17 "And Ananias went his way, and entered into the house; and putting his hands on him said, Brother Saul, the Lord, even Jesus, that appeared unto thee in the way as thou camest, hath sent me, that thou mightest receive thy sight, and be filled with the Holy Ghost.
18 And immediately there fell from his eyes as it had been scales: and he received sight forthwith, and arose, and was baptized." (Acts of the Apostles 9:17-18).
Note: Here we see Paul being baptized into the Spirit first by the laying on of hands, and then he was water baptized by Ananias (Who was a Jewish Christian who knew of the OT ritual Jewish baptism teaching).
Occurence #4.
1 "And it came to pass, that, while Apollos was at Corinth, Paul having passed through the upper coasts came to Ephesus: and finding certain disciples,
2 He said unto them, Have ye received the Holy Ghost since ye believed? And they said unto him, We have not so much as heard whether there be any Holy Ghost.
3 And he said unto them, Unto what then were ye baptized? And they said, Unto John's baptism.
4 Then said Paul, John verily baptized with the baptism of repentance, saying unto the people, that they should believe on him which should come after him, that is, on Christ Jesus.
5 When they heard this, they were baptized in the name of the Lord Jesus.
6 And when Paul had laid his hands upon them, the Holy Ghost came on them; and they spake with tongues, and prophesied." (Acts of the Apostles 19:1-6).
Note: Paul talks with believers at Ephesus who were only aware of water baptism via by John and hence they were not aware of the Holy Ghost. So Paul baptizes them into the Spirit by the laying on of hands in Jesus's name.
So I see two possibilities when Jesus said, "Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost:" (Matthew 28:19).
Possibility #1.
Jesus always meant to spirit baptize by the laying on of hands for all nations (Jews and Gentiles in all the world), but He allowed for his followers to misunderstand because water baptism was an important picture or symbol of Spirit baptism by the laying on of his hands (Which is the true baptism), until the time of when Paul would reveal the true baptism that was to be ultimately done (Which is made clear in Acts of the Apostles 19:1-6).
This is not the first time that Jesus allowed His followers to misunderstand him to fulfill God's greater purpose and plans. Jesus told his disciples to buy a sword, but He actually was referring to the spiritual sword (Which was the communicated Word of God, i.e. the Scriptures). By their misunderstanding, Jesus was able to teach Peter that he that lives by the sword shall die by the sword. Jesus undid Peter's wrong actions of hurting somebody with a sword by healing Peter's victim and He rebuked Peter saying that He could have called down a ton of angels to protect Him (if He truly wanted to).
Possibility #2.
The gospel was to the Jew first, and then to the Gentile. While the gospel was not fully realized yet, an early form of the gospel (i.e. Salvation in the Messiah Jesus) went out to only the Israelite cities before Christ's death. After Christ's death and resurrection, the gospel (in it's full revelation) was to go out until all the Jews in every nation (i.e. Matthew 28:19). Water baptism was a part of the transitional period practice taught by Jesus as a part of the Jewish customs taught by John the Baptist who was the last Jewish OT prophet. Water baptism was more of a Jewish practice (although Gentiles could partake in it if they wanted to - like with the Ethiopian eunuch, and Ananias and his family). So yes. Jesus commanded the Jewish disciples to baptize in the name of the Father, the Son, and the Holy Ghost in water, but this was primarily for the Jews in those believing nations (even though the Gentiles could partake of such a practice if they wanted to). So the command to be baptized in water is more of a command that applies if you are a Jew. For no Gentile believers were present among the original remaining 11 disciples when Jesus gave His command in Matthew 28:19. But Jesus was still pointing the most important aspect of baptism is Spirit baptism. For Jesus said that they will not be baptized in water, but they will baptized in the Holy Ghost, which would be at Pentecost (Which took place after Christ's ascension).