Sometimes you may find a family showing up in section view even if the section was not cutting the family.
This behaviour is controlled within the family in Visibility/Graphics Overrides.
Some Categories have the Show Only if Instance is Cut parameter unticked and greyed out so you can't change it.
The following categories DO have this parameter enabled.
There is a work around, but be aware that any sub-categories will be deleted if you change categories, so you will need to recreate them and re-assign objects to them.
To turn this parameter on in a category where it is not enabled create (or change) your family to another category, tick the Show Only if Instance is Cut parameter.
Then change your family to the category you want.