By default once a shared parameter is loaded into a project, the Group parameter under category will remain even if the group is later changed and reloaded into the project.
-You originally specify the shared parameter to be grouped under Dimensions in a family, and load it into a project.
-Later, in the family, you change the group to Construction and load it back into the project.
-The project still maintains the original Dimensions group even if the family is purged and loaded back into the project
You can change the group by temporarily creating a Project Parameter, point it to the Shared Parameter with the desired group, and then load the family back in. This will reset the Group parameter under category.