This is an example of supercooling – the process by which a very pure liquid is chilled to a temperature just below its usual freezing point without actually making the jump to its solid state. Bottled water is perfect for this, especially the kind that’s been purified via reverse osmosis, a process that strips water of all its particulates. This particulates can act as “seed crystals,” or “nuclei,” to which a liquid phase on the cusp of becoming solid can attach, and crystalize around. In this video, a seed crystal is introduced in the form of a cube of already-frozen water. As soon as it’s introduced, the liquid phase rapidly crystallizes and attaches to the solid one, kicking off a chain reaction of ice-formation.
Water that freezes as it’s being poured out of the bottle also solidifies upon exposure to a seed crystal, which, in this case, is an already-frozen surface. This is similar to the effect observed when freezing rain, supercooled by its flightpath through sub-freezing layers of atmosphere, comes into contact with an object cooled to a temperature below freezing. The result is a phenomenon known as glaze-ice, which – if you live somewhere cold – you may have seen before, coating the spindly extremities of tree branches.
See here for more on supercooling and glassy water.