Unfortunately I'm not able to reproduce the pagination bug on the link you provided either locally or in any of the other websites I manage, which leads me to believe it may be an issue with your theme or another plugin that is installed.
I recommend installing the WP Paginate plugin and testing again. If this plugin is installed, Clean Testimonials leverages it when rendering pagination given it has quite a few more features and is wildly popular.
Regarding the code change you made to output a certain number of testimonials per page, that's great, however when I release the next version your code changes will be overwritten. I have this planned as a feature for the next release, however.
As you can see, the shortcode attribute is "per_page". If you modify your own change to use this name as well, you won't have to change your shortcodes once I release version 1.3 shortly.