No, the water in toilets and bathtubs don’t spin clockwise in the Northern Hemisphere and counterclockwise in the Southern. It’s a myth.
There is something that’s called the Coriolis force, which affects huge bodies of water and tends to make them want to spin in response to Earth’s rotation.
But what works with huge oceans doesn’t work on the much smaller scale of bathroom fixtures.
Good thing, toootherwise you’d have to worry about your toilet overflowing twice a day at high tide.