Having air left over is not generally a function of breathing too deeply. It is a function of not getting and using the air correctly.
Step one: Longtones. Breathe in as deeply as possible and hold a middle G at medium volume - play til you run out of air. That works, right? What is the difference then between an Arbans exercize and a long tone? YOU! You are probably tensing up during breathing and staying tense afterwards.
Start your practice sessions with longtones and lip slurs. Breathe deeply and use all of your air. Get used to that feeling, then add articulation to the RELAXED playing. A teacher should be monitoring this, not some internet blogger with no real interest in YOUR progression.