Mail Delete Function in Web Mail

Tech Team: Most of the time I access my cox addresses via Outlook. Settings are such that the deleted folder is emptied on close. When I subsequently access my accounts for Cox WebMail, all the deleted email is still in the in box. The only solution I have found is use Outlook to move mail I want to keep, from the inbox to an off-line PST. I then come back to Cox WebMail, and delete everything. That seems to permanently delete all the junk that tends to accumulate in my inbox on Cox WebMail but not evident when I use Outlook. What am I doing wrong that prevents "delete" in Outlook from really deleting the items? Thanks, Pat Jordan