I am a new host - it took about 10 days for my response rate to show up. When it did, it was 100% - I don't know if the thing that made it show up was me responding to a certain # of requests, or if it is a matter of how many days. But I responded to a request on my first day, and nothing happened with my response rate until about day 10.
I also respond immediately to all messages, sometimes through text, sometimes through the airbnb app. I think the system understands/tracks both.