If you check before the handkerchief is dropped, regardless of how much time has passed, a minute of time is added into the cylinder and you get injected with it immediately. they can't just check right away and get a 0 second penalty, it'll be a minute at least, more if they had any previously stored time from earlier rounds. this is an unavoidable punishment. the accumulated time is just if you check late, you don't get injected, but X seconds get added to the cylinder (which will be injected either the next time you fail or when the cylinder fills).
the thing i would want clarification on is that Yakou says he will start the timer when the handkerchief hits the floor. what happens if you turn around to check right as the person is dropping it, in the split second before it hits the floor? would this just count as a 1 second accumulated time like in Yakou's scenario, or would it be a loss since it hasn't hit the floor yet?