You are incorrect in stating that it has everything to do with test tubes.
You must consider the time it takes for heat to spread throughout the volume of water, for one.
Also, is it all H2O in our oceans? Funny; I thought they were also comprised of a large amount of salt and other impurities, which affects density.
Also, it does not just say that which you said. It quantifies the rise as well:
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research showed sea levels would rise by between 0.4 and 1.4 metres simply because sea water would continue warming up, which makes it expand.
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Also, you are correct regarding evaporation, but then you also do not consider that as temperature increases the residence time of water in the atmosphere decreases, meaning that though there is an increase in the amount going up, there is also an increase in the amount going down.