If someone burns 400 calories in the gym daily one week on phase 2 and states that they are hungry, should the coach increase by only 1 serving of fat and reassess the next week? Or add 4 servings?

Burning 400 calories per day in Stabilization would be considered a “high intensity” workout, which is not recommended in Stabilization (but is highly encouraged in Maintenance.) And yes, calories “out” should be replaced via calories “in”.