My understanding of the mechanism for isotope ratios in ice cores is identical to yours. I am not an expert but when I got interested in GW I researched everything and found several academic sources that that provided equivalent explanations. But I was not aware that ice core analysis could go back much more than 5000 years.
Your reference is going back 5 million years based upon equatorial conditions so it is not about ice cores. From the text you provided I guess that the proxy is microscopic animal/plant residues from sunlight dependent organisms that lived very near the surface. That hypothesis leads me to think that the surface water isotope ratios are a compliment of the ice core ratios. In ice cores we see a difference because warm conditions evaporate more O18 from the water so in the water there will be less O18.
What surprised me it that they can actually detect a difference. I would have expected dilution and mixing within the ocean surface layer to quickly erase the difference. However what they are seeing is backed by ice core data so it has merit. I sure would like to understand the statistical methods they are using to extract signal from what must be very noisy samplings.