Interesting that using the recovery key stopped the issue for you, but does not seem to do its job now.
From the article "Ken said he enabled a recovery key for his account as instructed, but that it hasn’t stopped the unbidden system alerts from appearing on all of his devices every few days.
KrebsOnSecurity tested Ken’s experience, and can confirm that enabling a recovery key does nothing to stop a password reset prompt from being sent to associated Apple devices. "
A password reset prompt is sent to the devices, but unfortunately the article leaves out that the prompt only enables you to reset the password on the device that receives the prompt. So it is not a security issue, just an annoyance.
KrebsOnSecurity tested Ken’s experience, and can confirm that enabling a recovery key does nothing to stop a password reset prompt from being sent to associated Apple devices. "