King of Tokyo card question+ dice read
Yes, that's basically the point of the card.  Here's a BGG thread confirming it.
CyberBunny is not currently in Tokyo, so he is definitely able to heal.  And since he is not in Tokyo, the damage he deals is applied to monsters in Tokyo.  Since Gigazour does not leave Tokyo, CyberBunny is placed in Tokyo Bay.  So yes, your resolution is correct.