So we actually have an existing model for your problem of "hitting an exact time in milliseconds" - it's playing a musical instrument.

There is always a delay between playing a note and that sound appearing. In some larger instruments like the bass guitar or an organ, that time can be tens of milliseconds. But humans can compensate very well.

It turns out that the accuracy of people's timing has a named, called the Haas Limit. In most people, including a lot of musicians, it's about 10ms, but in some people, it's as low as 5ms.

This means that a competent musician should be able to hit your 1cs (centisecond) target fairly often, so your target time granularity is pretty well spot on!