Part of the reason is gravitational effects. When a large amount of ice melts, the Earth's gravity is shifted away from that region.
This gives you a sense of the absolutely huge amount of ice we're talking about. For example, if the West Antarctic Ice Shelf collapses we'll see about 10 metres of sea level rise, but mostly in the northern hemisphere. To underline just how much ice this is, this effect will slowly be counteracted as the ground below slowly rebounds (as it no longer has a huge amount of ice crushing it down from above).
Potentially related is the centrifugal effect - the Earth bulges at the equator slightly because of spin. Logically, melted ice would tend to cause water to "rise" more at the equators (further from the ice caps) than near the poles.
It's been done. I can't find the reference, but apparently the extreme accuracy of atomic clocks has proven that the mass of water moving from the poles to the equator has slowed the earth's rotation as predicted.
"rapid deglaciation promotes earthquakes ... rebound stress that is available to trigger earthquakes today is of the order of 1 MPa. This stress level is not large enough to rupture intact rocks but is large enough to reactivate pre-existing faults that are close to failure."
This gives you a sense of the absolutely huge amount of ice we're talking about. For example, if the West Antarctic Ice Shelf collapses we'll see about 10 metres of sea level rise, but mostly in the northern hemisphere. To underline just how much ice this is, this effect will slowly be counteracted as the ground below slowly rebounds (as it no longer has a huge amount of ice crushing it down from above).