I would be wary about sending a warning email from an email address that could be traced back to me. Some people panic, and assume that you're the person responsible, or lash out at the only person they can strike - you.
As per the box legitimate owner, while I agree that there is all kind of crazy out there and you can avoid this if it makes you uncomfortable (abuse-at-provider will most likely contact them shortly without involving you), I don't see the lash out or strike at you scenarios likely, in my experience usually you get a thank you.
To be clear, I'm not suggesting email "Bro, you are compromised, bye", I mean, you can just inform them that you received the link and were taken to a phishing site that looks like hosted on his machine, attach screens, advice them on next steps if you want to go the extra mile in niceness. You're doing them a favour without breaking any law, why would they get mad at you?