This behavior is probably the result of your email program on your local computer being set up as POP3.
If your email program and your mobile device are set up to utilize POP3, then each device will download "NEW EMAIL" from the server to that device.
You will see the emails in each place, because you're downloading a "copy" of the email to each device.
So when you delete an email on your desktop computer, it will still be on your mobile device. And vice versa.
This is "reassuring" to some people, as they like to know that a "copy" of the email will always be "archived" on their local computer. They can delete it from their MOBILE device, or from WEBMAIL when they don't need it anymore, knowing that they will always have a copy on their DESKTOP COMPUTER.
For people who simply want their INBOX to be the same on EVERY DEVICE, and be able to delete a copy of the email from the phone, and have that also be deleted from their inbox on their local computer, then they need to set up their EMAIL CLIENT on their Desktop Computer and their email on their MOBILE DEVICE as IMAP.
If planning to set up as IMAP, you should read up on what this entails before you decide to do that, as our Jub Jub server space is not unlimited. You can always upgrade to more space, but if you want to manage your email without having to pay for extra "cloud storage" you may simply want to keep your email set up as POP.