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Looks like it was, indeed, a DNS cache issue since the popup does not appear anymore on google search after clearing the cache. Still appearing when visiting the website though (which is perfectly legit by the way, as well as OP's), guess I'll just stop doing it ahah.. Noobie question here : is there anything these websites' managers/hosters can do about that ? For instance, would it be usefull to warn them about this issue or is it beyond their control ? Again, thanks a lot for your help

Well something I can add about this issue is that the Malwarebytes popup only appears when I'm entering the website on Edge/Explorer. On Chrome, it appears even when I make a research on google about that particular website (not everytime I search for smthg), and it's the only one concerned about this. So idk if you can draw any conclusion about that ? Also I just made a clean windows install a few hours ago so it would surprise me if I was infected with anything since I haven't gone anywhere on internet yet except youtube/facebook/etc. and this particular website. Thank you for you help by the way

Exact same message here for www.passeportsante.net. I even get the popup when I type the name on google research, so before even entering the website anyone knows what getviously is exactly ?