pageinate_links is a function that retrieves paginated link for archive post pages.
So yes – there are links. And links works exactly this way – if you click on it, you will go to the url that is connected with that link – so the page will get reloaded.
If you want the link to cause a partial reload of only one div (or other container), you’ll have to write your own code, that will:
- Prevent the link reloading the page when clicked.
- Send AJAX request to the server and obtain new content of that container.
- Replace the content of container with the new content received from server.