The earth is huge(compared to us), so it's hard to grasp why it doesn't work as seemingly instantaneously as bowl of water, for example. Eventually, in a perfect vacuum, that would be the case.
The changes that are producing the change in sea water volume, also have other effects on some of the things that influence sea water distribution.
For example melting freshwater ice not only adds volume to the ocean, it also adds mass, and changes salinity, which changes temperature, which itself affects volume, and also influences ocean circulation patterns.
And since winds are powered and directed by heat energy in the atmosphere, changing the amount and/or pattern of heat in the atmosphere will also change the wind patterns.
The shape of the ocean floor is slightly affected by the weight of the sea water on top of it. Changes in sea water distribution due to other factors might also result in changes in relative ocean basin depth--areas with more water mass will depress the crust a bit farther into the mantle; while areas with less water mass will rebound slightly.
One simple reason is that water tends to flow towards the lowest point. Since there are height differences on earth, distribution will not be even.
Another is that polar ice, through its gravitational pull, pulls water in the direction of the poles. If it melts, it (on average) moves away from the poles, decreasing that pull towards the poles.