I think your answer is on that page:
"Note that this argument applies only if the ice cube is made of the same water as the water that it is floating in. This is true, for example, with the Arctic ice pack, which is made of frozen sea water. However, it is not true for Antarctic icebergs, which are blocks of fresh-water ice from the continent that are floating in salt-water sea. In this case, we must take into account that the salt water is denser than the fresh water. The fresh-water iceberg still weighs as much as the weight of the displaced salt water, but because of the difference in density, the volume of melted fresh water will be slightly greater than the displaced volume of salt water -- so when the iceberg melts, the water level will rise, although the difference is very small.
If the ice is melting due to a rise in temperature of the water, then the water level might rise because of thermal expansion - related to, but not because of, the ice melting.
If the ice was totally or partly supported on the bottom of the vessel (or sea), then when it melts the water level will certainly rise. In the limit, if there was no water in the vessel at the start of the experiment, there clearly will be at the end, and it is obvious the water level has risen. This is a key problem resulting from global warming ? melting ice that was covering land areas such as Antarctica and Greenland is adding to sea levels."
(Note: I think this answers your question. Am a dunce about this sort of thing)