Are primary and secondary insurance claims are filed simultaneously to ensure prompt payment to the medical practice?

In general this is true. However, the insurance policies usually have "coordination of benefits" provisions which explain which policy pays first and under what circumstances. There are sometimes also statutes (laws) that dictate the order of payment. A good example of this is when one is injured in an auto collision and has both personal injury protection and/or medical payments coverage and health insurance. The companies will coordinate the payment of benefits as between the policies.