Indeed it is not an amphetamine. However, I’ve seen it referred to as one even in academic literature. It’s a nuance that many doctors probably don’t have the time to figure out. My own doctor tried to tell me that Ritalin and Adderall worked in the same way and neither is stronger than the other. This is not true, and I had done my research beforehand to know that. They each work a bit differently and Adderall is stronger per MG than Ritalin.
Drug stores sell home drug tests, and you will indeed see that there are amphetamine tests and methylphenidate tests (and some have both in one, but the package will say so). Your doctor have had previous experience with a test that looked for both, but he may not have been aware that it was a combo test, leading him to believe one test can always detect either.