seems to start his run to intercept the ball as you press the button,
Why should the AI wait until you press the button?
it feels like the AI reads your pad input on certain occasions.
See above, it feels that way but it's not. It takes some practice to be able to pass acurately behind defenders who sneak into passing lanes but it's well worth it when you get the hang of it.
that player will 100% turn in the opposite direction that you choose to go
My expereince is quite the opposite. the AI defenders in this situation lose the ball a little too often instead of clearing it out of bounds with their first touch or passing back to the goalie.
I can't stress enough that you have to pay attention to detail. For example here is one of many things that you could take into consideration in this scenario without going into detail. First and foremost is your own movement and positioning. If you are going to chase a player down you need to be directly behing him and only occasionaly feignting either side of him to confuse him, secondly you need to vary your speed when you get on his back. If your coming like a train on tracks all he has to do is get out of the way. I could go on about other factors, but the point is you have to take into consideration real life details instead of just doing an approximate rendition and expecting it to work every now and then.