This is an important and rather complex issue. The specific case that you raise, to my knowledge, involves an independent foundation that is not part of the government apparatus. So it's not something that would be of direct concern to CSIS.
That said, if we learned that a foreign entity was interfering through various means and targeting people inside or outside of government, we would have the authority to investigate that directly.
To answer the question more specifically, CSIS does not necessarily have the final say. Indeed, depending on the scenario, other agencies and organizations may be involved. However, in my experience, these issues are discussed with CSIS, which always has a say.