I also had this issue. When I used the plugin to change the order of posts, I wanted the posts to display in a specific order, like A. B, C … (not alphabetically, these are just labels). The posts display in this order in the admin (wp-admin/edit.php?page=order-post-types-post) and on category pages on the front end. Perfect.
I expected, then, that when you looked at the single post B, the “Previous post” would be A and the “Next post” would be C.
But the problem, as you pointed out, is that WordPress assumes that when you’re looking at post B, the “Next post” is A, not C. That’s why the post nav links on single post pages gave me the opposite result from what I wanted.
I fixed the issue by editing my child theme’s functions.php file. (I’m using a child theme based on twentythirteen.) I copied the code from the parent theme’s functions.php file that begins:
if ( ! function_exists( 'twentythirteen_post_nav' ) ) :
and ends with:
endif;
I then replaced:
<?php previous_post_link( '%link', _x( '<span class="meta-nav">←</span> %title', 'Previous post link', 'twentythirteen' ) ); ?>
<?php next_post_link( '%link', _x( '%title <span class="meta-nav">→</span>', 'Next post link', 'twentythirteen' ) ); ?>
with
<?php previous_post_link( '%link', _x( '%title <span class="meta-nav">→</span>', 'Previous post link', 'twentythirteen' ) ); ?>
<?php next_post_link( '%link', _x( '<span class="meta-nav">←</span> %title', 'Next post link', 'twentythirteen' ) ); ?>
Then I used css to swap the right/left placement of the nav links.
There’s probably a better way to accomplish this, but this method works.
BTW, the plugin author was very helpful, looking into the admin on my site and writing not one but two patient explanations of why this issue was happening. (To sum up: it’s WordPress, not the plugin). The plugin is very easy to use and works perfectly; I would rate it a 5 if the post-nav issue could be addressed via the plugin settings, which I’ve suggested could be addressed in a future update.