Yes, the official was correct to issue a direct technical foul to the Team A head coach for running onto the court without being invited. This action violates the rules of basketball.
The official was correct in his decision to issue a direct technical foul to the Team A head coach. In basketball rules, team personnel, including coaches, are not allowed to enter the court unless they are beckoned by an official. In a circumstance such as a fight, the official would typically first attempt to defuse the situation before calling for additional assistance. Since the Team A head coach ran onto the court without being beckoned, they violated the rules, justifying the technical foul assigned by the official.
Learn more about Basketball Rules