I just happened to look at a question I asked a month ago and noticed that an answer was posted a week after I asked the question. I was surprised to see an answer since I didn't recall ever receiving any notification that an answer was posted.
Sure enough, when I looked in my inbox, I didn't see any message from Code Review indicating that an answer was posted.
The day after I posted my question, a user added a comment, and I did receive an inbox notification for that:
In the responses section of my profile activity, both the answer and comment responses are there, however, there is only a message in my inbox regarding the comment.
I've received other answer notification from other Stack Exchange sites since this Code Review answer was posted, so this seems to just be an issue with the Code Review site or with this specific post.