Step by step:
1) I go to Appearance => Widgets
2) Drag the ‘Text’ widget to the ‘Right Sidebar’
3) Fill in the information for the text
4) Choose ‘Display Widget of Selected’
5) Choose the blog page called ‘Testimonials’ as the page to display the widget
6) Click save
7) Go to fresh instance of the blog page
8) The widget does not show up
9) Tried this with all of the widgets, including the stock widgets that come with WordPress
10) None of the widgets show up
Note: All of the widgets work with your plugin when I try them on the pages using the default template but does not work with the blog template for a page.
Stephen, if your blog page – the one where you display all posts, is Testimonials page, than (in terms of wordpress conditional tags) this is not a Page but Homepage.
Please modify your Display Widget of Selected setting and see if it works.