Southern Response have added the following information to their website (here), describing how properties with asbestos will be treated.
Before your repair work begins the main repair contractor will assess whether they need to test for the presence of asbestos in building materials in your home - based on the age, construction materials used and the nature and location of earthquake damage. If asbestos testing is needed, the main contractor will arrange for inspection of the earthquake damaged areas; This will be done at our cost.
If asbestos is identified in earthquake damaged materials, a competent contractor will be engaged to remove that type of asbestos product that is earthquake damaged.
The main contractor is fully responsible for asbestos identification, testing, removal and disposal as per the Ministry of Business, Innovation and Employment rules and Health and Safety Act.
We will advise you if asbestos is identified in earthquake damaged areas of your home and can give you a copy of the test results if you request them.
Further information on asbestos can be found on the Ministry of Health website: https://www.healthed.govt.nz/resource/all-about-asbestos