Pseudo-forces in this case are due to inertial effects that the cork experiences.
Initially, the entire system including the cork, beaker, liquid, metal and string are stationary. According to Newtons First Law of motion, these objects at rest will want to stay at rest unless a force is applied to them.
When you accelerate the beaker to the left, everything in the beaker initially has no force acting on it, and wants to stay at rest, but the beaker wants to move, and everything contained in it has no choice. This means the beaker will apply a force on the fluid and on the metal ball. These will resist, but the resistance will not be as noticeable, as the metal ball would require a decent force to move relative to the beaker, and the movement in the fluid itself wont be very visually apparent.
The cork still wants to stay in place too. As everything starts accelerating to the right, it wants to stay put. From the perspective of the beaker, that is the same as the cork going to the left. As the metal ball moves and the cork doesn't, this increases the tension in the string. Eventually this tension is enough to get the cork moving with the same speed as the system, but at that point the string will be at some angle which makes the cork to the left of the metal ball.