This is a long-running scam, and they often claim to be from "Windows support" to sound legit without actually mentioning Microsoft.
A good point to remember is that if someone cold-calls you about computer problems, it is ALWAYS a scam - there is no way an external organisation can find out about activity on your home or office network and link it to your phone number.
I first had them call about 5 years ago. I too run a Mac but my parents use windoze. I ran through their whole con with them pretending to do what they told me to do and acted dumb when they asked me 'what do you see'. They would then say 'do you see this?' and I would say 'oh yes'... and they would proceed.
What they end up trying to get you to do is to enter their IP address all allow it access to everything. Then they try and get your Credit Card number for ongoing support. (which I dutifully told them I had to ask my husband permission to use...LOL) They gave me a bogus call-back number.
At the time I wrote to the Dept of Fair Trading, the Sydney Morning Herald and the Byron Shire Echo. The Echo was the only party who published anything about it and it took another 2 years before there were any scam-warnings about it on the Dept of Fair Trading site.
It is a really sucky scam as it targets the elderly. They freak when they think they have a virus so don't stop to think about the legitimacy of the call. (I mean eg my mother deletes every email she writes after it is sent or received as she is so paranoid)
Sent from my iPad
11th Hour Group Pty Ltd
Thanks Rob, a very good point.