Individual responsibilities for each employee must be clearly communicated and understood by both sides, employee and supervisor. These responsibilities mush also be shared with the entire team as well as with other teams they regularly interact with. People need to know who does what and how they contribute to the entire team and the entire organizational mission, strategy and vision.
Additionally, organizational reporting structure must be clear and each employee/team can have only ONE direct supervisor. Having multiple supervisors can and often does create misalignment and uncomfortable and somewhat contentious situations which we should all avoid.