Inertia everywhere

Unfortunately your solution is wrong. Do the experiment again and watch carefully.
A hill of water is generated, in fact on that side which is not pulled.

Liquid substances (and gases) are inert, too. The water is in rest and would like to (just like the ball in the first experiment) stay in this position. If you move the tub, the water stays where it is. Due to the fact that it cannot flow through the back board of the tub, it impounds. A hill of water is generated. But the mass of the water pushes the (easily movable) particles of the water downwards respectively to the sides. A wave is moving to the other side of the tub and is reflected there at the board. This process is repeated several times until the water has settled again.