When does the ten second backcourt count start?

[Sharpshooternes]

I think we have discussed this before but I was just watching one of my videos from summer camp and it got me wondering about it again. Is it upon the release or upon someone, anyone, touching it inbounds?

My gut is saying it starts on the first touch so that it is possible for there to be some delay between the pass and the start of the count. After a timeout, and A1 rolls the ball down the court and then someone picks it up at mid court. I am pretty sure there is no count until the touch as the clock does not run either.
Does it matter after, say, a made basket?