On the contrary, Texas was part of the United States on June 19, 1865 and every day prior to that since she first petitioned for inclusion into the United States. The rebellion didn't change that.
A state is more than a political subdivision of a nation. Texas, a free, independent, sovereign nation, chose to become one of the united States. Later, Texas chose to dissolve that relationship. You can read the Texas Declaration of Seccession at http://www.yale.edu/lawweb/avalon/csa/texsec.htm