'Password for iCloud needs to be updated'

Hello there. I've recently updated my Apple ID with a new e-mail address. Since then my MAC keeps asking me to update password for the previous e-mail. Attaching the system pop up message. The old e-mail became the secondary e-mail. So I still have it in the list of e-mails (I think it is listed as a recovery e-mail) when I log into icloud.com . What is the problem? When I look up my iCloud account details on my MAC the old e-mail is listed as 'Verified' (whatever that means). If I try to enter my Apple ID password for this old e-mail the system says incorrect password.

Thank you for helping! Mike