You are three-fourths right. The States are not citizens, or the people, and the amendment refers specifically to "the people," not just citizens. There is no mention of "citizens" in the Ninth Amendment, but it does mention "the people." Citizens are a subset of "the people." However, the US Constitution does also references "citizens" specifically. As in Article IV, Section 2, Clause 1, the Fourteenth and the Twenty-Sixth Amendments, for example. Where ever the US makes a reference to "the people" or "person" (as in the Fourteenth Amendment) they are actually including everyone within the jurisdiction of the US - regardless whether they are citizens or not.
The phrase "the people," as in the First, Second, Fourth, Ninth, and Tenth Amendments, is a reference to everyone within the borders of the US. Their citizenship status or legal status does not matter.