Accessory muscle use is not a normal sign of respiration. We see these muscles used during times of respiratory distress. This is likely caused by an underlying pathological cause like asthma, but could also be from something as simple as anxiety or extreme physical activity. Accessory muscles come into play to help assist the diaphragm in moving more air faster, but they don't come without a price. Accessory muscle use is very fatiguing to the patient and if not corrected promptly, can lead to respiratory arrest.
Here's a quick reference for remembering the different areas in which we see accessory muscle use with inspiration and expiration.