No need for alarm. Taking the 10th Amendment to claim state sovereignty is not an act of attempt at secession or declaration of state independence. It's just reserving the state's lawmaking powers as provided in the Constitution of the Union, i.e. the Congress shall pass no law impeding individual state's rights to those laws. For example, social laws are under individual state's purview and power. Therefore, the individual states, not Congress, pass laws for marriage, divorce, abortion etc.
Good that you cleared that up. I think they mistook what the issue was.