Property Management - Charging insurance or Owner for disaster management

[Greg Virgin]

I manage a residential single family property for an owner. Last week a very large tree fell on the home causing significant damage to the structure and forcing the tenant to be relocated temporarily while the insurance claim is processed an the property is restored. As a manager, I have spent many additional hours coordinating things like tree removal, mitigation, restoration, and coordinating with insurance adjusters. My property management agreement doesn't currently include any provision about disaster management and compensation for additional time and resources dedicated to resolving large problems like this. 

My questions:

Is management of disasters something billable to insurance companies as a part of a claim? 

Do other property managers have recommendations on provisions that can be included within a management agreement to ensure disaster / major unplanned occurrence that consume time and resources are billable? If so, what is a typical fee or fee structure?