The value in the field is binary data. The custom settings only affect the way Notes diplays the data. They do not affect the data itself. The field does not store the custom format in the document. It only stores the binary value in the document.
Your computed field is working on the binary value. It has no knowledge of how some other field formats that value. So it uses the format specified in the machine's locale settings.
If you really want a text value with a specific format, write your own code to create the format that you want. Use @Year, @Month and @Day to get the components of the date.
You should be aware that hard coded formats tend to confuse users. If a user has set the client machine's preferences to display dates in a certain way, then it is a good idea to respect those preferences. Otherwise dates in your application are displayed inconsistently from dates in other applications. Users will make errors as a result.