The integration in a web browser on a PC is quite good. But on my Android device it doesn't happen the same; despite having installed both apps don't communicate with each other.
Is the integration of both apps planned?
No, Chrome for mobile devices is not compatible but Firefox does support add-ons. I have it installed on my mobile. It does not help me at all, of course.
Anyway, there is a way to connect Tmetric with Asana on mobile devices: Firefox.