I've been a moderator on a couple of other websites (and am still modding at one of them) and dealt with many "sockpuppets"---people who create multiple accounts, or create second or third or more accounts after the previous account is banned.

Yes, we tend to be immediately suspicious if we note the same IP address for several different accounts, and usually bring down the ban-hammer after we've given them a chance to explain. The troublemakers are pretty easy to spot, though---most are dumb enough not to know that we can figure out who they are by their posting styles. Occasionally, however, we investigate and find that the member lives with others who also visit the site and use the same computer, and those we'll let go.

I think that's what happened with the mods at your site---they likely checked out your story and it added up, so they'll probably leave you guys alone. You can always clarify it with them, and a good moderator will be glad to answer any questions you may have. Don't be afraid of them; they are not just there to police the site, but serve as resources and guides.