When you copy a report.. only the report itself is copied... all the segments point to the same segment ids (whether they are permanent segments or adhoc/report only segments). You can see this by looking at the ID in the URL when you go to edit your segement....
This is actually a good thing (in most cases), because I will often create very specific complex segments to support a need (that I don't want to make fully permanent) in the components area (as they can only be used in very specific breakdowns)... but IF I need to make a change to the logic, all the reports that were based off of the original get the updates.
This also works the same if you have a segment in a table and you copy that table and make changes to the table in the report... if you need to change the segment, you don't want to make those changes for each table that is using the segment... that would be a lot of work, and prone to manual error depending on how many times the segment is used.
IF you need to make report specific segments when you create a copy of a Workspace, you will need to create a new segment and replace all instances of the other segment. This is the only solution. When I train people on building workspaces in my organization, I always stress this point to them.