Are you logged in with a google account on that chrome/chromium ? By the way, how did you install them ?
To resume :
On your debian computer, only for this website, you get redirect to ads only with chrome/chromium ?
I would try these :
purge chromium and chrome.
Install chromium and go to your website. (do not log in before).
The only things i can think of is broken extension. I've never see this happening, it's really strange. If that happens on windows i would have say, search for malware and delete them.