Obviously, there are different points of view; some Americans believe the Constitution (including the Bill of Rights) means "exactly what it says." Others believe in a more expansive and flexible interpretation...
“the 10th Amendment was cited by the seceeding States in support of their formal severance of ties.”
No, the 10th Amendment was not cited by any of the 11 seceding states in their Ordinances of Secession.
Five of the seceding states wrote documents laying out the reason and justification for their decisions to secede from the Union. Not one of those documents cites justification under the 10 Amendment to the Constitution. In two of those documents the Constitutional article cited is Article IV, Section 2 clause 3 (aka the fugitive slave clause). One state cites Article IV section 2 clause 2. One state cites Article 7. No where in the primary documentation of secession is Amendment 10 of the Constitution mentioned.