Anyone can have more than one account here (even though it's frowned upon), simply by registering under different usernames (with different email addresses). If you use more than one web browser (such as having Firefox and Chrome running simultaneously on a PC), you can easily switch from using one account to another. (e.g. you could submit a trolling post with one username and then immediately respond to it, apparently as a completely different user, by swithcing to the other browser/username).
When looking to see whether a site user is logged in or not, AB's server looks for a cookie on that user's web browser. When you logged out on your PC the log-in cookie will automatically have expired but there was still an active log-in cookie on your iPad browser, meaning that any traffic coming from there was seen as 'logged in' by AB's server.