It's not news that the Crown Prince's knights and the magicians of the tower didn't get along. The main reason why was because of the atrocities that were pinned on the capes of the aforementioned magicians.
The late third concubine, the Crown Prince's mother, was said to have suffered endlessly from the pain of her sickness. Instead of physicians, the magicians were given the duty of healing the third concubine. That was a point of suspicion for the nobles who were on the Crown Prince's side.
The diagnosis for the third concubine was that she had a curable lung disease. The physicians of the Imperial Family were adept in curing such sickness, so it would have made sense if they were tasked with the woman's health.
Sending the magicians was a peculiar move by the Emperor. The presence of magicians would only bring about complications to the method of healing. The physicians alone could accomplish the healing in a timely manner.