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Those links seem very helpful, thanks. The solution you linked seem to have been merged in Turpentine since 2015 already, yet I still have the issue. I will try to edit the .vcl config as suggested here: github.com/nexcess/magento-turpentine/issues/…
Found it, although there's a warning that says: "Force requests to be for a specific domain name, will probably break most multi-store setups". Which is exactly my case, I have a multistore setup.
The file exists (Setup.php), but that's a core file, so I guess it's being used by the extension for something. app/code/community/Wyomind contains nothing relevant. I guess I'll check the database and see what I can find. The devs assured me that it's an optional part of the extensions, so it can be removed without impact on the extension working state