Let's separate these out, and start with 96146. That code is for automated testing and automated results. That means the test is taken on a computer by the patient, and the computer formulates the results. No interpretation is needed, and no one "administers" it.
As far as the provider administering the other test, there are two choices for psychological testing by a physician or other qualified healthcare provided (meaning, not a technician or computer) . One is 96130, which is psychological testing evaluation services... first hour. The other is 96136, which is psychological test administration services (2 or more)... first hour.
So the question is, did the provider do any evaluation , including integration of patient data, interpretation of standardized test results and clinical data, clinical decision making, treating planning and report, and any interactive feedback to the patient/family (evaluation)? Or did he merely administer and score a test? (administration)