If you are loading the posts and pagination via ajax, then your pagination links need have listeners attached to them that make ajax calls of their own. Right now, it appears you are loading normal pagination links, and that's not how your page is designed to work.

Three steps:

1. Add a 'paged' variable to the data object in your ajax call so that this information is passed to your php function.
2. Adjust your php function so that it outputs custom pagination links
3. Add new javascript that listens for clicks on these links and makes your ajax call with the paged variable set appropriately

EDIT: On second thought, you don't need step two as you can probably attach your event and gather the page information from the links as they are.