OnSong automatically moves through songs in your set if the Autoscroll Through Set setting is enabled. With this enabled, when you start autoscroll, OnSong will advance to the next song in the set after the bottom of the first is reached.
To disable this setting, go into the Utilities menu by tapping on the foot pedal icon. You can then choose Settings > Live Settings > Autoscroll and turn off the Autoscroll Through Sets.