If you make the up tube large so that the speed is arbitrarily slow, then you won't have flying droplets,
rather the water would just dribble out of the end of the pipe. With a garden sprinkler and jet, as water exits the sprinkler jet, pressure energy is convert to velocity head. In the siphon, if your pipe is large and there is no jet, then there will be no flying droplets. You need either the water to be travelling at a reasonably speed if there is no jet, or you can have a large tube and slow speed if you fit a jet, however, as noted above, pressure energy is converted to velocity head energy as it travels through the jet, with the smaller jet size giving it the speed necessary.

So the answer to what makes the droplets fly through the air is velocity head energy.