The don't come through despite been deleted, they have been downloaded to your computer BEFORE you deleted them from the web interface!
Outlook is configured to use the POP3 protocol with the option of leaving the messages on the server turned on.
It also seems that it was left running and set to periodicaly fetch new messages as the came.
POP3 batch download messages to the computer and usualy delete them from the server immediately, but it can be set to leave the messages on the server.
Set Outlook to use the IMAP protocol instead. This will enable automatic synchronising acros multiple devices and access modes.
When using IMAP, if a message is deleted from the server using the web interface, it's also deleted for any other devices.
Electro
February 2015