When The statement in Acts 11 was made, Cornelius had had the Spirit fall on him "and" had already been water baptized.
13 And he reported to us how he had seen the angel standing in his house, and saying, ‘Send to Joppa and have Simon, who is also called Peter, brought here;
14 and he will speak
words to you by which you will be saved, you and all your household.’
15 And as I began to speak, the Holy Spirit fell upon them just as
He did upon us at the beginning.
16 And I remembered the word of the Lord, how He used to say, ‘John baptized with water, but you will be baptized with the Holy Spirit.’
17 Therefore if God gave to them the same gift as
He gave to us also
after believing in the Lord Jesus Christ, who was I that I could stand in God’s way?â€
I do not see anywhere that Peter is saying that Cornelius was already baptized in water. Quite the contrary is taught in Acts 10 and he repeats it here in Acts 11 by his vision. That gentiles could also receive the Holy Spirit and therefore, be baptized in water.
Before this revelation of Peter's at the house of Cornelius
Gentiles were not baptized in water by John the Baptist or anyone. It was viewed as only for the Jews.
Acts 10:44
New American Standard Bible (NASB)
44 While Peter was still
speaking these words, the Holy Spirit fell upon
all those who were listening to the message.
I propose, that it was not the presence of the apostles that caused the Holy Spirit to fall on "all who were Listening" but the power of God's words, the message from God.
When we receive the Lord "the circumcision of the heart" it is not the preachers presence that causes us to receive but the Words of God, the Message of the Gospel. "God's Words are sharper than a two-edged sword".