The idea that water rotates differently in the different hemispheres is a long-standing one. The Earth is subject to Coriolis forces, which determine how moving objects are deflected off the inside of rotating objects—wheels, circular containers, those kinds of things. Applied to Earth’s rotating sphere, the Coriolis effect accounts in part for why, say, hurricanes and cyclones rotate the way they do. (The storms rotate counterclockwise in the Northern Hemisphere and clockwise in the Southern.)
Here’s the catch, though. Coriolis forces are best observed at a large scale; toilet water, in so many ways, is small-scale. In your tub, such factors as any small asymmetry of the shape of the drain will determine which direction the circulation occurs.
Even in a tub having a perfectly symmetric drain, the circulation direction will be primarily influenced by any residual currents in the bathtub left over from the time when it was filled. It can take more than a day for such residual currents to subside completely. If all extraneous influences (including air currents) can be reduced below a certain level, one apparently can observe that drains do consistently drain in different directions in the two hemispheres.