This is 100% a scam. This person was not working for Apple and Apple would never call you for no reason, you would need to contact them first.
This is what is known as "phone phishing" it is can be a very serious problem if you do let them access your computer.
Basically what they will do is call a lot of phone numbers and say that you have problems. Any actual computer problems you have will be entirely coincidental. Usually what they will do is show you things that most computer users would not understand and say that they are problems or viruses.
Next they log onto your computer and lie to you about the numerous problems they pretend to find. Next they will attempt to get you to pay a few hundred dollars to "fix" the issues when in fact they actually do nothing useful.
Always remember, no legitimate tech support company would ever call you. Your computer does not report to Apple or any other company so if any tech support person calls you can trust it is a scam and just hang up.
If you are actually having issues with your mac then I would advise you take it to your local apple store or find a certified apple repair company in the area and call them. Again any time tech support calls you first it is a scam and they just want to charge you hundreds of dollars. They usually lie and often sound like they are from another country such as India and their English is not very good.
Have a look at this article from the FTC about these type of scams: https://www.consumer.ftc.gov/articles/0346-tech-support-scams
If they call you again simply hang up, do not speak to them at all. If you need real help contact your local apple store, if you don't know how to do that let me know what city and state you live in and I will find a certified tech for you.
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