The scripture says when the GENTILES heard that they were now included and able to have salvation... they began rejoicing. Why do you think they were rejoicing? The Gentiles were just told that they could now have a relationship with God; they could now have eternal life. The Gentiles used to be excluded, and without God in the world, see Ephesians 2:12.
HOWEVER, NOW they were told they could have salvation! All those Gentiles who were there who heard the good news, that Gentiles as a race of people could now have eternal life, they believed. Gentiles as a nation of people were appointed to eternal life, not all Gentiles will have eternal life, and only the Gentiles who believe will have eternal life. The Gentiles who were appointed life---all those there at that time believed.
Acts 13:48 When the Gentiles heard this, they were glad and honored the word of the Lord; and all who were appointed for eternal life believed.
There were Jews AND Gentiles in the crowd. All who were appointed [the Gentiles] in the crowd, all of them there believed.