Fastest recorded visual reaction time in any animal was 0.015s (15ms) for a tiny fly to sudden bright light. The general rule is it increases with the physical distance a signal needs to travel across an animals nervous system and the complexity of what’s being responded to.

So, while I don’t have exact measurements on hand ~50ms is good enough for an internet comment.

Accurate human throwing requires a timing accuracy of 1 ms.

Precision of 1ms not timing of 1ms. It’s just like taking a step you can chose when to start but you need to synchronize motions after that point to maintain an efficient stride.

In the end that kind of precision is extremely easy for nervous systems as the lag just gets built in. Which is how hummingbird hearts can do 21 beats per second with different timings between each of the 4 chambers at sub 1ms precision.