Looks like timing problem. You may improve it by doing empty hand techniques against weapons.
Every time you get hit in the head with bokken, you will improve your timing
The answer to your whole post, is like he said:
It only takes years of dedicated practice to learn.
When to start moving? if you start half a second earlier, you can move way slower, but if you start too early, you should get a wack on your head.
So, how to discern the intent of movement before the move? practice to be soft (in your mind) and in a few years (10, 15 or 20) it will probably come to you.