Part 25 RTO actions often have a 1 second buffer added to them, but that's not just a recognition/reaction thing, the guidance also talks about 'normal variations'. It can also be the case that delay times are specified in the performance rules just to add conservatism in distances, not because the pilot reaction is expected to be that long. (And hence the perf and handling assessments for a similar failure end up with different timings)
I've seen, but can't pin down a reference as yet, numbers like 1 sec or 3 sec used as "recognition" times, based on how "in the loop" the crew are when the failure occurs, and then a further 3 seconds used as a "reaction" time to decide on, and take, a specific action. But those tend to be for "non-instinctive" reactions and recognitions - no one applies any of those as delays for something like VMCG, controlling the direction of the aircraft is instinctive and immediate. I was expecting to find those timings in either AC25.1309 or Ac25-7, but haven't tracked them down, though they may be in there and I missed them.
As a comment, I'm not sure I'd use the word "startle" in this sense, as I've seen it used in cases where it was also an inappropriate pilot reaction that was being discussed, "response" is probably a much better word, as you use in the body of the post.