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It looks like the pages that you're referencing in the Webmaster Forums post do have some indexed duplicate content on them. It may be that Google is trying to figure out which version of the page is the canonical version, and then reporting all the duplicates as links back to the page that they deem the "original" page. I don't know why they would report this as a "link" when it clearly isn't a link in the traditional sense, but link reports in Search Console often contain some weird stuff that isn't really links. What's clear is that Google understands that these pages are related, which makes sense since it's the same content, on pages with very similar design - the two subdomains are even using the same Google Analytics account. My assumption would be that the "links" are a byproduct of Google trying to figure out which of these pages are the duplicates and which should be treated as the original. It may be that this is nothing to worry about - if you're happy with the pages' performance, I doubt you will see these "links" coming through anywhere besides Google Search Console. If you do want to keep the client sites more separate, I would recommend separating them out into their own Google Analytics accounts at the very least.