Your email is downloaded and synchronised via your Mail Provider's mail servers - and not directly between devices.
Each device will independently download Mail from your Mail Provider's incoming Mail Server - and keep an independent copy of the mail messages on each device. Your device settings along with the type of email account will largely determine what happens when an email message is deleted.
So as to determine a probable cause as to why message deletion is not occurring on your iPad, you will need to provide more information.
Does your Mail Provider use IMAP, POP3, or something else? Are you receiving the same email messages on all devices? Perhaps you can receive but not send email from one or more devices?
If all devices that can access your mail account are configured to use IMAP - and can all send and receive email - then all devices should remain synchronised when an email is deleted; a deletion from one device will result in the corresponding copy of the email message being deleted from all devices.