The chakra you gain at start of round does not trigger chakra coordination hp gain. Only skills that gain you extra chakra do so, and even then only for the ninja generating it. Examples include wind main's natural draining (a good combination with chakra coordination for that precise reason), sage naruto's 20 chakra gain at time of action, and samui's 15 chakra per cloud ninja attack (note that the 15 chakra actually comes from the ninja making the attack, not samui despite the ability originating from her, so the attacking ninja will be the one that is healed).