Regular pop up alerts: “Device Added to Your Account”

I'm not alone with this, and it's only a minor annoyance, and I can see other similar queries, but apart from re-starting the machine, nothing helps. I switch on or open up one of our Macs, I receive a pop-up message warning me that there's been a "Device Added to Your Account" with a security warning.

• No, I have not been hacked.
• No, I haven't added a new devices (and those flagged up are not "new")
• Nothing has changed about my Apple products

Is anyone here seeing this? Have you managed to solve it? Can you help.please?

Steve