Automated call claiming iCloud impact; press 1 for tech support, etc. guy wants me to go to fast support.com which switches to Google and then wants me to let him access my computer. Am I correct to assume this is a scam?

Has anyone received an automated call claiming that iCloud has been compromised and asking you to press 1 for tech assistance? After pressing 1, the person answering was able to provide ID info including name and direct number, then wanted me to go to fast support.com, which then switched to google.com (I use only Safari), and at point the next step was to allow the support person to enter a code and access my computer to help identify any phony users on my iCloud account. I begged off, assuming this was a scam. Would like to know if this has happened recently to anyone else, and if I am correct in not pursuing the matter? (Since i have iCloud on my phone and defunct iPad, I assume whatever happened would affect all)