The effect is known to be more easily achieved with distilled or deionised water. The chemical impurities in tap water impair or slow down the rate at which ice crystal is deposited by blocking off some of the hydrogen bonds. The effect is that instead of maintaining a slightly warmer interior than exterior, all of the water cools to the same uniform temperature too quickly and cools uniformly, and so expands uniformly when it freezes.(The rate of spread of low temperature throughout the water is higher than the rate of freezing in the area first exposed to cold air.)
What happens when it works is that (using distilled water) the edges/rims of the fluid surface in the container cool quicker than its centre (from room temperature) (like with soup,etc)(when placed in a freezer, ie surrounded by cold air) because it is in 'contact'/'mixing distance' with less fluid than the centre (on one side is not fluid but the container wall which is not warm) and so has a lower heat replacement rate to compensate for that which is constantly lost to the cold fridge air. An ice donut shape forms with a hole in the middle where the liquid is warmer. As freezing continues the hole slowly shrinks and the existing ice inceases in thickness downwards - staying frozen to the height of the original water level. The downward expansion of ice into the container forces the water out (since the volume available in the container is decreasing) and up the hole in the centre of the surface of the ice, forming a rounded drip of water that bulges out of the hole. Again the cooling rate is higher on the edges and so a ring of ice forms around and follows the shape of the base of the drip-shaped water bulge, but the water is continuously being forced out, by the formation of more ice in the container and the usage of container volume by the ice (which takes up approx. 10% more volume that water). New rings of ice, that trace the base of the drip shape, form and create a tube which the water volume continues to be forced up. A column-like tube of ice is the result and this continues to grow in length until there is no more water rising up the ice tube, since it has all frozen. The tube and all the fluid in the container is now solid ice (the drip/bulge at the top of the water column has frozen).
The angle of the column or spike of water is determined by many small almost uncontrollable factors such as air and water currents, the shape of the container, the temperature of the freezer, the material and thickness of the container, if the container is tilted during formation and if there are any vibrations while it forms - such as from a freezer compressor pump motor, or an impatient poking finger. : )