By design, the Pull to Add Page feature reuses the first/last page's template for the new page.
To add a page that will instead use a built-in template:
1. From the document view, tap the Add Page icon near the top-right corner.
2. Tap Before, After, or Last Page to indicate the position of the new page.
3. Tap a template in the list, or tap Templates in the header to choose another.