The question is well answered by Aaron and Emilio. To make the effects interesting, let us visualise the scenario for a particular case - when the object is hydrophilic (water attracting) and air resistance is negligible, in a qualitative manner.
The following image shows the system at different times:
The "Initial State" as the name suggests is how the system looks immediately after flipping. The second diagram (from left to right) shows the system after some time. You could see, near the bottom, the liquid near the beaker's inner surface has moved lesser distance compared to the liquid near the axis of the beaker. This can be attributed to the viscous forces of water which acts in between different layers. Think it of as a frictional force between different layer of the fluid. At this time, near the top, a somewhat "nothing" vacuum gets created much like when "mercury barometers" are tilted.
Let us assume that this suction force due to the vacuum (more precisely the atmospheric pressure at the bottom pushing the liquid upwards into the beaker) is not enough to hold the liquid inside the beaker itself.
The third image shows the situation at a later time. Till now both the object and the centre of mass of the fluid has fallen down at the same rate. The object could have moved downward slightly more than the liquid due to attraction forces provided by the molecules of the liquid. This is best observed in the fourth image. By this time, the entire both water and object have come out of the beaker.
Now, the situation will be similar to having no gravity. As we've neglected air resistance, water takes nearly a spherical shape. Further, as the object is hydrophilic, attraction forces balance out only near the centre of the water sphere and so, the system will look like the last image denoted by "Final State".
In reality, if we include air resistance, we may have to account for the distortions in the spherical shape of the liquid. Also this might alter the position of the object inside the liquid.
It seems some do not understand why the object moves towards the centre of the liquid sphere. To eliminate this confusion, let us consider the following diagram, which shows the adhesive interactions between molecules of water and the object in red coloured arrows:
The object placed off centred, has a non uniform distribution of water molecules around it. So, the distribution of forces is also not uniform and hence net force is towards the centre. You can imagine this like different people pulling the object using a rope with equal forces but the number of people on different directions is different and hence causing a difference to the state of rest of the object.
It was asked in the comments how can something not in contact with the ball exert force? How can the force be unbalanced?
The reason is adhesive interactions are electrostatic forces. These reduce with increase in the separation between the interacting objects. Further, these forces can act even if there is no physical contact between them.
I'm not saying the object at an off-centred position goes towards the centre of the water sphere due to "hydrophilic" interactions. It's because of the "adhesive forces" which act between the molecules of water and the object. Adhesive forces can act even if there is no physical contact as they are electrostatic in nature as described previously.
The main source of confusion in the comments below was misunderstanding of adhesive forces as hydrophilic interactions. The main reason why I considered hydrophilic objects over hydrophobic is: in the case of hydrophobic objects due to the initial state of the system, the object would remain out of the liquid and the liquid would not swallow the object due to adhesive interactions as repulsive forces are stronger than attractive forces.
If the hydrophobic object were swallowed the energy of the system increases or in other words it'll be less stable and so the object and the liquid fall down as separate entities.
Image Courtesy: My own work :)