Typically that happens when you did not actually change the address on an account but instead created a new account. The apps have to be updated when signed into the account that downloaded them originally. Did you truly change the email address, or did you unintentionally set up a new account? To truly change the address:
The support article Change your Apple ID - Apple Support outlines various methods for changing the email address (Apple ID) you use for your Apple Account while retaining everything in your account.
If you have an iPhone or iPad:
1. Go to Settings, then tap your name.
2. Tap Sign In & Security.
3. Next to Email & Phone Numbers, tap Edit.
4. Tap the Remove button next to the email address, then tap Delete.
5. Tap Choose Another Email Address and enter your device passcode if asked.
6. Enter the new email address, then tap Continue.
7. Enter the verification code that was sent to your new email address. Read this support article to learn what to do if you didn’t get the email —> If you didn't receive your verification or reset email - Apple Support
8. If you encounter issues with certain services after doing this, this outdated support article may still have useful suggestions --> What to do after you change your Apple ID or password - Apple Support
Refer to the support article Change your Apple ID - Apple Support :
- If you don’t have an iPhone or iPad the support article says to, “go to https://appleid.apple.com and sign in. Then follow the onscreen instructions to change the email address associated with your Apple ID.”
- For general information, and other issues such as changes or addresses not being accepted.
- Note a recent change to the article where you can now change the email address without having to have access to your old email account.
If you mistakenly set up a new account, delete it, go back to using the old account and change it properly. For information about how to delete an Apple ID account, read this support article —> How to delete your Apple ID account - Apple Support
Carefully and thoroughly read that article for information about what happens when you delete your Apple ID account. For example:
"Make sure that you sign out of all your devices to avoid issues with apps that use your Apple ID account or iCloud. After your account is deleted, you can't sign out of iCloud or turn off Find My iPhone Activation Lock on your devices. If you forget to sign out, you might not be able to use your device when your account is deleted."
If you need to go back to the old account and want to change the address, you will find you cannot use the address you used to set up the new account. You will have to use an address Apple hasn't seen before.