During the time of Jadzia Dax, there was a time travel episode that came back to the era of James T Kirk and gang. During the episode, Jadzia Dax removed her trill spots to make her look like a human Starfleet officer. Since there is special rules for non member races to join Starfleet, there may not have been any Trills at that time as members of the Starfleet.
If Trill was not a member of the Federation during the 2240’s and they were during the era of Jadzia Dax during the 2360’s, it begs the question when they did join.
If Trill was not a member of the Federation during the 2240’s and they were during the era of Jadzia Dax during the 2360’s, it begs the question when they did join.