SYMPTOM
When duplication is performed across project sources, if the destination project has no privileges assigned to the 'Everyone' group and the users in the destination project are assigned privileges through security roles only, the 'Everyone' group in the destination project acquires the privileges from the source project in Strategy Desktop 8.x. This occurs when the 'Project-related users and groups only' option for user/group duplication is selected.
STEPS TO REPRODUCE
Consider a project A belonging to project source PS-A. The 'Everyone' group in PS-A is assigned 'Desktop Analyst' and 'Desktop Designer' privileges. Consider a user 'X' with 'Desktop Analyst' and 'Desktop Designer' privileges. The user 'X' has access to project A.
Consider another project source, PS-B. The 'Everyone' group in PS-B has no privileges assigned to it.
Project A is duplicated from source PS-A to destination PS-B with the users/group duplication option as 'Project-related users and groups only', as shown below:

After duplication, the 'Everyone' group in PS-B will have 'Desktop Analyst' and 'Desktop Designer' privileges.
CAUSE
When the option of 'Project-related users and groups only' is selected during project duplication across project sources, the users in the source project need to be moved to the destination project. Since the users in the source project are assigned privileges through the 'Everyone' group, the privileges of the 'Everyone' group in the source also need to be moved over to the destination.
ACTION
User can avoid the 'Everyone' group in the destination from acquiring privileges from the source project in either of the following ways: