When the car is stationary, the aromatic liquid in the bottle is quite mobile and changes its horizontal position as the bottle is tilted. At the same time, when the car is moving, the liquid level remains parallel to the bottom of the bottle as it oscillates. Why does this happen?

 

If you keep it simple, by ignoring ripples and waves, then the force on each particle is effectively the force of gravity, so each particle tries to get as low as possible. That's what gives you a flat horizontal surface. Tilt the bottle, and the same thing applies. Any particle that's higher than the one next to it will sink a little, so you still end up with a flat horizontal surface. (relative to the Earth)

When the car is just rolling, without braking or accelerating, the same applies. But when you brake or accelerate, you add an effective sideways force to the pull of gravity, so you still get a flat surface but it's tilted. It's as if you've tilted the pull of gravity, by adding the sideways force. Turning left or right has the same effect.