Safari Compromised Password Popup

Well, the popup you received and the fact that you have password issues are two separate things. The popup may not have been legit (I can't find how Apple notifies users of password issues when using Safari) and you could have been taken for a very bad ride.

Now, independent of the popup, you saw that you have passwords issues: you know what to do and, most importantly, safely, because you are not clicking on a dubious link.

It most likely is not legit. You should review your passwords yourself by going to Safari > Preferences > Passwords and look for the yellow triangle icon that warns you of password issues.