Customer Success reporting to Product

Yes, I would say if your team were being managed by product then the KPI's are different, for example product adoption. This is typically when you are smaller, and you are trying to have customers find value in product. Once your product is established you will want to create KPI's that deliver value to revenue. They would be CSM qualified leads, upsells, and engagement for example.

I have seen this in early stage, only sporadically. The reasoning - product needs to be connected / responsible for the outcome of the success in the field. As you grow, this needs to change.

Javed