iCloud does not sync email accounts. What determines if deleting an email from an account deletes it from another device or computer is whether the account is POP, IMAP, or Exchange. Read/deleted/sent messages on an IMAP or Exchange account will sync. Not so on a POP account. iCloud supports IMAP, so if you have a @mac.com, @me.com, or @icloud.com email address, the changes will sync. If you made your 3rd party POP account an iCloud account that does not change it suddenly to IMAP.