How can I conditionally show different home page templates based on whether or not the user is logged in?

First check that there isn’t a page set as a front page in “Reading Setting”. If that is set, index.php is not used as the home page, but the template of the page you set as front page.

In that case, you need to find that template and add you conditional is there.

<?php
if(is_user_logged_in()) {
 get_header(); ?>
<div id="primary" class="content-area">
    <div class="primary-inner">
        <div id="content" class="site-content content-list" role="main">
        <?php 
        if ( have_posts() ) : 
            while ( have_posts() ) : the_post(); 
                get_template_part( 'content', get_post_format() ); 
            endwhile;
            dw_minion_content_nav( 'nav-below' ); 
        else : 
            get_template_part( 'no-results', 'index' ); 
        endif; 
        ?>
        </div>
    </div>
</div>
<?php get_sidebar('secondary'); ?>
<?php get_footer(); ?>
<?php } else { ?>
    YOU CAN CREATE A PAGE TEMPLATE HERE THAT WILL SHOW IF USER IS NOT LOGGED IN
     YOU CAN ALSO ADD A LOGIN WIDGET HERE. 
<?php
} ?>