Now I might come off as a hater, which won't hurt me, but I gotta point out I think you're deliberately seeing more than there really is. Of course he sees right moves and feels the tempo here and there, he's a well-taught crack. But his awareness is far from impeccable. For instance, in one of his last sub appearances, kept running for the ball ("press", even though not) all the way across the field from the left to the right side of the pitch leaving a HUGE gap behind him. Opponents failed to take advantage due to their clumsiness and nothing else. Elementary school backyard football that. Some of it due to willingness to prove himself, rest due to reckless positioning.
It's very understandable if he does stuff like that, or if he tries the killer ball more often than what's optimal. Both because of his playing time situation, and because of Koemans comments - Koeman wants him to play more directly "in front of the player", arrive in the box, and I am sure he wants him to press like a maniac as well?
I don't like these pressing runs over too large distances, but this is how it's done - even Busquets keeps pressing to the goalie when he has started his run. Optimally he should be able to hand the press over to someone else, but the most important thing is that there is press on the ball. A good lackmustest for how good Barcelona is, is the intensity of - and the willingness to - press.
I think he has the ability to both press intensively, and to win the ball. How often he does it, and over which zones, should be easy to fix. But I enjoy to see someone who is like a dog when the ball is near, like Pedro or Alves. I haven't seen much of what you describe, but of course he will make mistakes, every player does all the time. I like his style very much, and it is probably true that my judgement is colored by that from the start.