Is support.me a scam or real virus support for apple products?

Whilst doing some google searching my browser suddenly started talking to me and warning me I had contracted a virus. I thought this strange as I hadn't opened any attachments or visited anything dodgy. The pop up window gave me a number to call for assistance in fixing my computer. I called but was very unconvinced by the 'support' person on the other end. She instructed me to force quite, upon which I say a safari programme not responding. I shut everything down and restarted my computer as per her instructions. She then told me to go to support.me and download something to fix my computer. At this point i got very suspicious and did a phishing google search on support me. A few warning posts on forums came up. So I told the woman I didn't trust her or the situation enough to continue so put the phone down rather than go to support.me. I feel vindicated but am still worried by whatever caused the pop up window in the first place. should i be? do i need real apple support to fix this? or did i catch the scam in time and I'm safe to carry on?