I have setup two websites, and then I would like to setup operators for a specific website, and not for both websites. Is that possible?
Yes, it is possible to appoint operator for a specific website in PRO plugin version.
Login into your www.wp-chat.com dashboard–> Settings–> Operators. In column “Access” select “Yes” or “No” and click “Save / Update”
Please, have a look at the attached image.