Hi kurtHS,
Thanks for using the Apple Support Communities for support. It's my understanding that you are receiving an email communication advising you to update your payment method for iCloud, but when you do this, you do not see confirmation of the update. I can see how this may cause some confusion, and I am happy to provide you more guidance.
There are a few ways you can change, add, or remove Apple ID payment methods. Some of which are through Settings on an iOS device, or using iTunes on your Mac or PC. In your post, when you mention step 1 states use Settings, it's likely referring to using an iOS device. Since you are using a Mac, that would not be applicable. Learn more about how to manage your payment methods here: Change, add, or remove Apple ID payment methods - Apple Support. Once it's updated, you can go back and check on your payment method via one of the mentioned ways, and see the changes reflected appropriately.
I do feel a bit curious about the email communication you are receiving, and I would like to confirm the validity of the email, as it could be a phishing attempt if it is not from Apple. With that said, I would like you to review this support article which will help you Avoid phishing emails, fake 'virus' alerts, phony support calls, and other scams. Also, Identify legitimate emails from the App Store or iTunes Store. Using these articles, will help you confirm if that email communication you are referring to, is even from Apple.
If you determine that email is not from Apple, but you have already submitted your personal details through links in the email, please reach out to your financial institution for help on handling this situation, and also speak with our iTunes Store Support team to report the information you had given out related to your Apple ID account: Contact - Official Apple Support.
Please let me know what you find, and if you have any further questions.
Cheers!
