I want the sidebars to show on some pages that I have used templates on. Is there a way to code that into my template? When I put <?php get_sidebar; ?>, it adds an archive list at the bottom of my page.

In ATO>Style & configure Sidebars you can select what pages they don't show on.

It is set to show on all pages. I think they are not showing because they are templates. The pages that I don't use templates for are just fine.

How did you build your templates?

I started with a template 'category.php' from the 'zenlite' theme, and removed what I didn't want.

This is a forum for the Atahualpa theme. You would need to check on their forum for help with that. If you are saying you use their php file as the starting point for an Atahualpa template then you are definitely going to have problems.