It's probably just an exercise in splitting hairs, but Pans Ops procedure design criteria includes 3 seconds delay for pilot reaction. Thus, any time the procedure requires the pilot to do something like initiate a turn or a missed approach climb, there is 3 seconds of delay built into the protection area. Again, there is no suggestion that the pilot should delay taking the action, of course.
I wonder if FAA's Terps uses a 2-seconds delay? It might be interesting to try to work out whether the 2 seconds is more realistic than 3 seconds. In any event, some delay is inevitable because it will take some time for a pilot to recognise the need to take some action and then initiate it.