@Adrienne174 As far as I know, both parties should get a notice that the other has left a review.
I'm not sure what you mean, that you don't see the review the host left- until both parties leave a review, or 14 days pass, you won't see the review the host left for you.
Under your inbox Airbnb messages, you'd probably have to switch to "travelling" messages from hosting messages to see the review notification?
Personally, I think it's kind of tacky for the host to tell you he's given you a 5* review. How does that strike you?