Key word, "almost." Taking the incompressibility of liquid too literally could mislead one to think that liquid in a sealed tube could be used for faster than light communication.
I imagine that much would depend on the shape of the bottle and the kinematics of the shaking. If it's a perfect cylinder, and the shaking is perfectly aligned with the axis of the cylinder, then perhaps no mixing would occur*. But if you shake a plastic soda bottle, the nubbins on the bottom would make areas of lower and higher pressure, which could induce turbulence. Also surface effects would be interesting -- either oil or water could be stickier, which could result in films, then droplets, being separated from one fluid into the other.
* though, shockwaves could conceivably form circular vortices...
There is no "not ... at all" in physics. Liquids have, strictly speaking, a very very low coefficient of compressibility, but are not absolutely incompressible.
