and when I write the NC and their manager comes back to me and says "what should I do" how do I counsel them? I'm part of the internal quality team so I can't just say "it's not my problem." They will expect advice from me on how to address the NC.
First, you have to define responsibilities and authorities and competency.
This done by using job descriptions, here you describe with some details what you need of your people, from here compare what in your people comply against this.
In areas they are weak, give the the appropriate training.
Job descriptions are also useful when hiring new people, is the filter to evaluate if competency is fulfilled.
On the other hand, your people shouldn't have to ask you what to do
It is supposed they are involved into the qms, regarding , training, corrective actions, they should know what to do, ok , you my guide them, but a qms is comprised of all the people in the organization.
Regards.