The coriolis acceleration points constantly to the center of sink's tied system, vector v is tangent to the circle, w is going from the southern pole to the northern pole.
What I am saying, is that the cycle itself is caused by physical aspects, rather than the rotation of the Earth. Thus the fact if you are in Britain or Australia, doesn't affect the side the water cycles since it's neglect-able to the acceleration caused by gravity.
I never said it would "stop" the particle, only that it would be as strong enough as to counter Coriolis force (or acceleration rather, m does divide out if you go for forces anyway), thus the assumption of north/south and turning-side is, well, wrong, given the fact it's deprived from Coriolis acceleration.
And I thought it out myself during a lecture in Dynamics about dust particles movement in a turbulence. EDIT: My teacher also confirmed this true, though he said my numbers are slightly off (I got a smaller degree, the numbers I used here were his after fixing a few things), even though I was off by a factor of 10^-2, the degree is still VERY small.
EDIT 2: What I meant with that, in summation, is that Coriolis force is so neglectable in compare to gravity. The example of the sink in an ideal system would simply create an harmonic movement, but since the particle is also having its radius changing as it slowly sinks in the sink, it gets a bigger end speed
I hope it's better explained in this way, sorry for any confusion I might've made.