I had a call from a similar person-Microsoft tech .I received error messages. Indian English. I asked him for his telephone number. He kept dogging. I persisted. Finally I told him I got you into a prolonged conversation because you are been monitored.
This is a scam. They got my personal details and started searching my computer for "tax" related info (think ssn). I called my credit card company and apple and they will be working with law enforcement authorities as necessary.
I should also mention that they said the "network" I'm on has been hacked by "foreign" IP addresses and even tried to show me one IP address from ny and one from ca and that they had to clean up the hackers out of my system "for only $199". They said they were Apple authorized technicians which they are not.
If they where in your computer, change any and all passwords and download and run malware bytes. Run your antivirus also and back that up with a online check like Nortons or McAfee (I think they still have online scans). Another good back up is Spybot Search and Destroy, both it and malware bytes can be found on filehippo. Update Spybot right off then run (do not use the tea timer).
If you had any information kept on your computer such as your social security number, date of birth or drivers license make sure you register with identity protection notify the credit agencies as well as your banks!!
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credit reports: Experian, Equifax, TransUnion
http://www.consumer.ftc.gov/articles/0155-free-credit-reports
The only persons who should be touching your computer is you, your manufacturer, Real Windows support that you have called and/or maybe a real live tech you see face to face!