Page Templates automatically showing index page contents?

If the code you posted above is all of your file contents then Yes you are missing something!

you just created a new page template but it’s empty, you need to tell WordPress what to display, and usually its done using the loop and a few other template tags add this code to you a.php under what you already have :

//this will include the theme header.php file
<?php get_header(); ?>


<div id="content" class="widecolumn">

 <?php if (have_posts()) : while (have_posts()) : the_post();?>
 <div class="post">
    <h2 id="post-<?php the_ID(); ?>"><?php the_title();?></h2>
    <div class="entrytext">
        <?php the_content(); ?>
    </div>
 </div>
 <?php endwhile; endif; ?>
 <?php edit_post_link('Edit this entry.', '<p>', '</p>'); ?>

</div>

//this will include the theme footer.php file
<?php get_footer(); ?>