Hello Teknofilo,
Thank you for using Apple Support Communities! I understand that when you read or delete an email in the Mail app on your iPhone 11 Pro, the action is not reflected on other devices when you access your email accounts. I would be happy to help provide steps to take next.
Were these accounts added to your iPhone as an IMAP or POP account? If they were added as a POP account, it can be expected behavior for changes not to sync to other devices once the emails have been downloaded to your iPhone from the server. If you aren't sure if you're using IMAP or POP, here's how you can tell:
If you can’t send or receive emails on your iPhone, iPad, or iPod touch - Apple Support
"If you have a POP3 email account, then you can only check email on one device at a time. Close other email programs and sign out of webmail sites that you have open. To check if your email is a POP3 account, go to Settings > Passwords & Accounts, tap your account, tap Account, then look for the label POP Account Information. You can also check the recommended email settings for your POP3 email account in the Mail Settings Lookup tool."
Using the Mail Settings Lookup link in the section above, you may also want to confirm the accounts have been added to the iPhone using the recommended settings. If it does not show the recommended settings, contact your email provider to verify this information.
If you have verified the email settings are correct, and the accounts have been added as IMAP, see if there's any change after updating your iPhone to iOS 13.1:
Update your iPhone, iPad, or iPod touch - Apple Support
Keep us posted on the results.
Cheers!
