When Smith writes about legal citizenship and lived citizenship, he is giving a general analytical framework. He is not saying only:

“This happened to formerly enslaved people after the Civil War.”

His article explicitly says that it uses the United States as its example, and its framework concerns the relationship between legal citizenship and lived citizenship more generally.

So there are two levels:

General proposition

Legal citizenship and lived citizenship can be distinguished.

This is Smith's conceptual proposition.

Your historical application

This distinction helps explain why formerly enslaved African Americans could acquire legal freedom while not immediately enjoying equal social, political, and economic standing after emancipation.

That is your application of Smith's framework to a particular historical case.

You can absolutely cite Smith for the first proposition and then apply it to post-emancipation America.

What you should avoid is attributing your exact second proposition to Smith unless he actually makes that specific argument in the passage you are citing.