The video is likely fake.
Watch closely how he pours the bucket. We don't see him pour it the first time. However, the second time, he pours it into the left side of the sink (from his perspective). This causes the water to have a clockwise motion (since it flows upwards on the left side). The second time, he pours it into the right side of the sink. This causes the water to have a counterclockwise motion (since it flows upwards on the right side). It is likely that the first time, he poured it into the middle. The nature of the hoax is covered in more detail by astronomer and skeptic Dr. Phil Plait at The Bad Astronomy Blog
There is a similar trick I saw in Kenya, where they turn one way before putting a bucket down on side of the equator, turn the other way on the other side, and put it down without turning at all in the middle. Dr. Phil Plait also covers this hoax in his book, Bad Astronomy (google books link to the chapter)
While TheBlackCat's answer (+1) is fully sufficient, this letter that appeared in Nature describes the authors experiments which show that (in Boston) if you set up the experiment very carefully, you can show that the Coriolis force reliably dictates the direction in which water drains from a basin specifically designed to negate other influences (see also southern hemisphere replication in this Nature letter). However, the rotation was only counterclockwise if you let the water settle for 24 hours and only started 12-15 minutes after opening the drain. The interesting fact is that the letter concludes:
"Incidentally, those who claim to have seen the direction of swirl change as a ship crosses the equator are surely pressing the case too far. At the equator the Coriolis forces vanish, and it would be virtually impossible to perform a valid experiment a short distance from the equator" [emphasis mine]
The Coriolis acceleration is proportional to the sine of the latitude (see e.g. wikipedia) so the last place on Earth the direction of draining would be dictated by the Coriolis force would be a couple of meters from the Equator.
So yes, we can be certain that the demonstration in the video is a trick, in the sense that it is not a legitimate demonstration that the direction of the vortex is governed by the rotation of the earth. The Coriolis effect is way too small to have created a vortex of that speed that quickly, and also the effect vanishes as you approach the equator anyway! The effect in this case is almost certainly due to the fact that the water is poured into the basin from the side that produces the desired vortex direction. This is something that was dealt with in the properly performed experiment by pouring the water into the vessel to create an initial rotation in the wrong direction, that would have to be overcome by the Coriolis force.