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FWIW, I have 4 Arban books in my studio. ALL THREE treble clef versions show in inverted turn (down first). However, the bass clef Bowman/Alessi version shows an normal turn. I think a player could make either one work. In the very old editions (for voice and other media) I see just a little squiggle, but it goes up before it goes down.
This is a notated folk song, and I have to think folk singers not using music may have ornamented all kind of ways on various notes, and then editors later added... who knows what. Just make it sound good!