Version 1.3 of Custom Single Post Templates Manager has been released. The fixes include compatibility with child themes and removal of the site wide links.
The plugin looks for the templates in the parent theme’s folder and then the child theme one. Unfortunately, the way the child theme check was done didn’t work properly, but this has now been fixed.
If you are using a child theme, make sure to be consistent with where you having a subfolder for the templates in order to avoid any problems with the wrong file being loaded. (On this site, I use a child theme and stick with placing templates in a subfolder of it.)
The plugin can be downloaded from WordPress.org.
If you’re experiencing problems, then leave a comment here or request support at the plugin’s WordPress.org support page.