Oultook 2016 - Stop applying categories across shared mailboxes
You need to know that Outlook categories is not more than a text field (property) of any Outlook item including message. This means that when you apply a category to a message, Outlook writes this category name as a text right to that message. This is why everyone can see it. And you can't change this behavior, sorry.
The category list you see in Outlook (with colors) called Master Category List. And it just allows you to see colors for matching category names.