My friend used my referral link and booked a reservation, but neither of us see the $20 credit that was advertised. What is going on?

Rover doesn't answer any questions here. Try calling them at [Edit: Rover’s contact options have changed. Visit the Rover Help Center at https://support.rover.com/ to find the phone number, help articles, or chat with the team] to get this straightened out or explained.

BTW, you will not get your $20 until after that stay has been completed as you yourself wrote. Booking a stay is not the same as completing.