From what I could infer from this article, it seems that
"Rabbi Leon (Yehudah Aryeh) Modena (1571-1648) was one of the most
colorful figures in the Jewish Renaissance. He was an accomplished
musician, and served as cantor in the Italian Synagogue in Venice. "
He encouraged integrating Rossi's music as part of the service. He met with considerable objection, apparently. There was a general accepted notion that music was forbidden after the destruction of the Temple. He argued against this opinion.
For Rabbi Leon Modena, his young friend, the musician Salamone Rossi,
would herald the Jewish re-awakening.
For there has arisen in Israel (thank God) … a very talented man,
accustomed to performing with singers before princes, dukes and
nobles. After the splendor of the people had been dimmed by the
passage of days and years, he restored their crown to its ancient
state as in the days of the Levites on their platforms. He set the
words of the Psalms to music that was published, joyous songs before
the Ark on Sabbaths, feasts and festivals. No longer will arrogant
opponents utter bitter words about the Hebrew folk. They will see that
it too possesses talent, the equal of the best endowed.
The article is not overly long, and it is fascinating to read about the various halachic objections that arose and how Rabbi Modena countered them.