How can I add a new page in the pages tab that belongs to specific theme?

Pages are an independent entity separate from whatever theme is active at that moment.

This is the design paradigm of most CMS systems that separate the concerns of site content from the view or rendering layer which allows a site owner the chance to change how his site looks without having to worry about the contents.

HOWEVER, it would theoretically be possible to build a plugin or simply hook into the template activation system within wordpress to activate or de-activate certain pages on the fly… Or the plugin could conditionally render menu’s based upon the active theme slug.