The only reason I can think of as to why you'd end up on your profile is that the inbox itself links to your profile. That is, the button on the topbar is also a link to your global inbox on your stackexchange.com profile - if you somehow managed to click it before the script loaded, or if you right-clicked it and selected "open in new tab (or whatever Safari offers), that'd give you your inbox instead of whatever you meant to open.
The answer was deleted, which is why when you were able to follow the link you couldn't see it. The real bug here is that you could still see the answer in your inbox: normally that would've been quietly removed from your inbox after the answer was deleted. But lemme back up a minute...
Whenever a new answer is posted, an event fires that adds the answer to the question owner's inbox. If the question doesn't have an owner - because, say, it was migrated to a site where the original owner doesn't have an account - then the system tries to track down the owner by following the migration history back to wherever it was migrated from. If it can find the owner, it still adds the notification - this way we don't leave folks hanging when their question is migrated before being answered!
When an answer is deleted, the process is very similar to what is described above: the system tries to track down the owner, follows migration history if need-be, and then removes the inbox item from the owner's inbox. Except, it also checks to see if the question is unowned and skips that removal step if it is... So you still got notified, even though the answer was deleted and there's zero chance you could've seen it since you didn't have an account on the site where it was posted!
Recommended fix: don't skip removal if we were actually able to track down an owner.