Magnolia is used in Chinese medicine, but usually is found in formulas for coughs and/or depression. Coughs can vary greatly and so herbs used in combination for coughs are usually more efficacious than a single herbal used for a cough. This next is a short discussion of how the type of cough determines the use of TCM herbal formulas:
China Herb Company - Bronchitis
"Next, you will want to ask the patient to cough for you so you can hear what type it is. If it is a dry cough, you may wish to add more of a moistening agent with a yin tonic. To loosen the cough, add Lung Yin tonics, such as Mai Men Dong (ophiopogon) and Sha Shen (Glehnia)."
"In general, the intake gives you information about which herb and formula to use. You want to know the quality of the cough, whether it hurts, if it is worse when lying down (indicating excess and possible post-nasal drip), and if the ribs hurt (Mu Hu Die or oroxylum will relax and open up the ribcage, functioning like acupuncture points Liver 14 and Lung 1)."
There is further discussion in the article about how types of cough are diagnosed and herbs are chosen using Chinese medicine. Magnolia may or may not be included for a cough depending on the type of cough.
Magnolia also may or may not be a part of a formula for depression. It would depend on whether the type of anxiety or depression would be helped by an herbal formula which contains magnolia. Magnolia is not chosen on Western based studies of herbs used as doctors would use a Western drug for depression or anxiety. Instead an herb is chosen by symptom picture and included in a formula which takes into consideration all the symptom picture of the individual patient. Here is the type of symptom picutre which would suggest the use of a formula which contained magnolia as one of a combination of herbs effective for the patient's symptoms:
Medic-acupuncture - Depression
"Obstruction by Static Qi and Phlegm: Clinical Manifestations: Discomfort in the throat as if obstructed by a plum pit, relief brought neither by coughing nor swallowing, sensation of congestion and blockage in the chest, costal pain. Tongue: White slimy coating. Pulse: Wiry, slippery. Treatment Method: Regulate qi, transform phlegm, dissipate binds, relieve depression. Herbal formula: Pinellia and Magnolia Bark Decoction "ban xia hou po tang".
So magnolia used alone may or may not help each individual. If it does not help or symptoms worsen then it is probably better to stop using it.