Generally NPS are sent out to execs. But NPS (or product NPS) are delivered to the end user. I am going to assume that you are talking about NPS from a stakeholder or an exec and give recommendation.
- As soon as you receive a detractor NPS, someone should reach out. I say someone because it can be automated and look like coming from an inbox or it can be actual person responsible for the customer (CSM, AM etc).
- Gainsight recommends that the outreach comes from the Manager in fact and not the specific CSM. This is done so that if there is a concern around the CSM experience, the customer is able to have a frank conversation. For a high touch, mid-market segment, it is the manager who reaches out with a prepopulated automated email template apologizing for the experience and asking if the exec can throw light on the issue or be able to meet them.
- From what you gather from the conversation from exec, you would need to course correct the customer by opening a risk CTA (in case of Gainsight) and then working with the Customer team in your organization to drive that risk to closure. If it is a larger issue that needs more cross-functional attention, that risk should be escalated and appropriate steps are taken.
If it is a product-related NPS, absolutely bring the product manager and product leadership in to get to speak with the customer. Best practices says that one of the customer facing metrics that Product Managers should be measured on is the Product NPS.