The word "they" and "their" refers to the Jews who lived in Jerusalem. Here the word "us" includes Paul and his entire audience in the synagogue. (See: [[rc://en/ta/man/translate/figs-inclusive]])
This can be stated in active form. Alternate translation: "God has sent the message about this salvation" (See: [[rc://en/ta/man/translate/figs-activepassive]])
The word "salvation" can be translated with the verb "save." Alternate translation: "that God will save people" (See: [[rc://en/ta/man/translate/figs-abstractnouns]])