Is an ad hom only personal

I’m in a discussion where a tweet was posted making a claim. In the discussion I copied and pasted a counter argument from a fact check site. People immediately attacked the fact check site and not the counter argument that was presented. I called this an ad hom. They said it wasn’t because they weren’t criticizing my personal character. My response was to think of me as a nuetral observer, I wasn’t making the argument the fact check site was. Who is correct here?

Hey Geoff, (This seems to have gone unanswered for some time.)

It's difficult to be precise without knowing what was said about the site in question, or directed to you personally. Off hand I'd say this does not qualify as a classic ad hominem, because it appears the argument was about your source and not you personally. I do suggest you peruse Dr. Bo's excellent list of ad hominem variations. To answer your question: no, there are a wide variety of ad hominem attacks and arguments that are not necessarily directly personal. See:
Ad Hominem (Abusive)
Ad Hominem (Circumstantial)
Ad Hominem (Guilt by Association)

I do see some potential areas of fallacious reasonings. such as

Irrelevant thesis - A fallacy of distraction that addesses a tangentially related (and perhaps valid) point that is not the point under discussion. Or, if the site is a Fundamentalist Christian site they could be making an Appeal to authority or even false authority. It depends, but we can't nail it down without knowing the details of the claim. It's possible that they're making a legitimate critique of the website in question and not just a personal attack against you.