Q: Does only damaged area need to be contained when fixing the lumber under roof?

Yes.  The renovation firm is responsible for containing the work area so that no dust or debris resulting from the disturbance of a painted surface leaves the work area while the renovation...

Yes.  The renovation firm is responsible for containing the work area so that no dust or debris resulting from the disturbance of a painted surface leaves the work area while the renovation is being performed.  Containment is not required for portions of the renovation outside this area that do not disturb painted components.  For exterior renovations, cover the ground with plastic sheeting or other disposable impermeable material extending 10 feet beyond the perimeter of surfaces undergoing renovation or a sufficient distance to collect falling paint debris, whichever is greater, unless the property line prevents 10 feet of such ground covering. Ground containment measures may stop at the edge of the vertical barrier when using a vertical containment system. If the renovation will affect surfaces within 10 feet of the property line, the renovation firm must erect vertical containment or equivalent extra precautions in containing the work area to ensure that dust and debris from the renovation does not contaminate adjacent buildings or migrate to adjacent properties. Vertical containment or equivalent extra precautions in containing the work area may also be necessary in other situations in order to prevent contamination of other buildings, other areas of the property, or adjacent buildings or properties.