Harvest is the only time tracking app with a “deep” integration inside Asana, meaning it is officially integrated into the interface. As of toady, I don’t know any other app deeply integrated, and none inside the mobile apps… However time tracking was part of the Unveiling the Future of Asana • Asana video, so maybe this is coming!
Would you be ok with a third-party time tracking app showing your tasks? I have listed a few on The ultimate guide for doing things with Asana