You can find server setting through the following link: https://www.timewarnercable.com/en/support/internet/step-by-step/twc-mail.html
Thanks! That woked. but when I delete messages on outlook for mac they don't move to the trash can there still on my inbox when I signed into mail.twc.com
In your settings on Outlook , you can choose to leave a copy of the message on the server. This is the option that you have selected if the messages are not being deleted from your mail box at https://mail.twc.com/.
The following LINK will provide you with instruction on how to change your settings on Outlook.
The user said they were using IMAP email but the link you sent them to was for POP, which handles deletions very differently. The basic question is still open - why aren't IMAP emails after being moved or deleted from the inbox on an IMAP client being deleted from the TWC server?