The strange behavior you're witnessing is not typical of pure water (and that includes water observed in super slow motion). The phenomenon is known as "the gobbling drop effect," and was first observed and recorded just three years ago by a team of researchers led by MIT's Gareth McKinley. So what's the secret to these droplets' column-climbing abilities? Polymers.
Turn on the tap at your sink and the water coming from the faucet will develop a waviness, causing it to dissociate into a stream of droplets. Most of us have seen this before. But when you add small quantities of polymer to that water, things get a little wonky. Fuck Yeah Fluid Dynamics explains:
The viscoelasticity of the polymer chains creates a force that opposes the thinning effects caused by surface tension. So, instead of thinning to the point of breaking into droplets, a drop is able to climb back up the jet until it reaches a critical mass where it reverses direction, accelerates downward due to gravity and eventually breaks off the jet. Then the whole process begins again with a new terminal drop.
We've talked before about the strange effects that polymers can have on fluids, so if you're still a little confused you can check that out here, but here's the upshot: When FYFD mentions "the viscoelasticity of the polymer chains in the water," he's talking about the the strength of the chemical bonds that keep these molecular chains linked together. These cross-linked chains are bound together so tightly that they're able to exert a force that countervails the weight of the fluid. The end effect is so dramatic, that it contradicts what we expect to see from liquids that we're more familiar with — like water.