Rust lists Steve Raymond as playing alto sax on this date and it's possible he was the one who doubled on tenor.
This is a great record and it's particularly notable for the way the various soloists build on each other's work instead of playing their own thing without regard to what came before. It's also an indication of the influence of Jewish klezmer music on jazz, which came in largely through the work of Jewish-American clarinetists like Benny Goodman and Artie Shaw. When klezmer had a brief revival as a folk music in the early 1980's I remember thinking, "So THAT'S where Benny Goodman came from. All the parts of his style he didn't take from Black New Orleans jazz clarinetists came from the folk music of his own people -- DUH!" The most obvious example of Goodman playing in a klezmer-influenced style is the portion of the 1937 "Sing, Sing, Sing" in which he's backed only by Gene Krupa's drums.