In King of Tokyo advanced play, does the monster in Tokyo Bay move into Tokyo City if the Tokyo City monster yields?
No, Monsters do not move from Tokyo Bay to Tokyo City.

In a 5-player game, there are multiple possible outcomes when you are attacking Tokyo City and Tokyo Bay.


If neither Monster dies - The attacker occupies Tokyo City , since you are still playing 5-player. The Monster in Tokyo Bay can choose to yield or not.
If the Monster in Tokyo City dies - The attacker occupies Tokyo City, and the Monster in Tokyo Bay must leave per the rule you quoted above, because there are now only 4 players.
If the Monster in Tokyo Bay dies - The attacker occupies Tokyo City if the Monster in Tokyo City yields.
If both Monsters die - The attacker occupies Tokyo City , since you are still playing 3-player. Neither Monster can choose to yield, because they are dead.