The relationship between the pitching coach and the pitcher is a very special one. The pitcher will probably never have a closer working relationship with management than what he has with his pitching coach. When you've gained their confidence you can go to work.
Teaching is a talent that is acquired and takes time.
So, when you begin your work with a pitcher you observe first before making changes. When you do your work in the bullpen, have something to specifically work on. Mechanics, a certain pitch, location, etc. Don't just throw - this is a waste of time. At this time is where you will do your critiquing - sometimes it requires being blunt, but not cruel.