Which property controls the changes in cost and resource plans with respect to the change...

According to the ServiceNow documentation1, this property controls whether the start dates of the resource plan, cost plan, and benefit plan are automatically updated when the start date of the demand or project is changed. If this property is set to true, then the plans will be shifted by the same number of days as the demand or project start date change. If this property is set to false, then the plans will not be affected by the demand or project start date change.

1: https://docs.servicenow.com/bundle/vancouver-it-business-management/page/product/project-management/reference/r_Properties.html