And I don't think Uhura would be following him were the situation not unique. She's his friend if nothing else; and he obviously needs her at those couple of moments.
Ya, getting shouted at, mocked and racially insulted by Kirk after losing his mother and his home planet is not enough for her to stop Kirk from doing what he did. Heck, she just accepts it later like 'whatever'. Does she go to Spock afterwards? No.