See here and here for the official info on the @ reply system.
Reason 1 is not correct; you will receive your notifications whenever you are logged in on an SE site (if you mean email notification, that is something you have to opt into; however the "about me" section does not affect this either).
Note that only the first three letters have to be a match; so reason 2 is definitely not it (in fact when typing an @ reply, the system provides you with a list of users in the comment thread, for convenience; all of its suggestions take the user name and strip the spaces).
Regarding reason 3: the notifications are displayed in the global inbox on the upper left corner of the site; a notification will look like
(that is where you can set up your email notifications if you want).
So, as far as I can tell there should be no reason for you not to have been notified. However I do have a guess: seeing that QiL's comment was edited, perhaps the original comment had the @ reply in a situation where it would not work, and then it was edited to its current form; if the system doesn't know to recheck a comment for new notifications after an edit, you wouldn't have received one. But I don't know if that's what happened, or if that's how the system works.