I have to confess I am slightly confused by this question. One party notifies (either Contractor or Project Manager) and then the Contractor provides the quotation. I am not sure where you(Contractor) are now describing this event other than in the quotation? If the Project Manager does not believe the quotation has been assessed correctly then they can make their own assessment (in line with what they believe the correct description of the event is).
My overriding advise here is talk! If you are having regular compensation event meetings, you should be updating each other on any event that is moving through the notification/quotation/assessment/implementation phases and hence should be no surprises/mis-interpretation.
My overriding advise here is talk! If you are having regular compensation event meetings, you should be updating each other on any event that is moving through the notification/quotation/assessment/implementation phases and hence should be no surprises/mis-interpretation.