reversed post navigation order but category listing order needs to change too

Hi everyone!

I hope you can help me (V.V)

My problem: I reversed the post display and navigation order from showing the latest posts first to showing them last. I had to reverse the single post navigation in order for it to navigate in the reversed order too.
But now, that I look at the posts in the category listing I see that it hasn’t been reversed as well >> BUT only visually. Meaning, where there should be a button to navigate to the right there’s nothing. Instead the button on the left side is displayed. But when I click on it it actually shows the right follow-up page! The pagination with numbers is working just fine btw. It’s only the arrows.

Here’s the category page I’m talking about (scroll to the bottom to see the navigation): my comic pages listing
And here’s the code I allready changed in my theme’s code (I simply replaced all $next with $prev):

<nav class="navigation single-page-navigation" role="navigation">
    <?php
    $prev = get_adjacent_post(false,'',false);
    $next = get_adjacent_post(false,'',true);
    ?>
    <div class="nav-links grids">
        <?php if( is_object($next) && $next->ID != get_the_ID()): ?>
        <div class="nav-previous grid-6">
            <a href="<?php echo get_permalink($next->ID); ?>"><i class="fa fa-chevron-left"></i> <?php _e( 'Previous Page', 'stag' ) ?></a>
        </div>
        <?php endif; ?>

        <?php if( is_object($prev) && $prev->ID != get_the_ID()): ?>
        <div class="nav-next grid-6">
            <a href="<?php echo get_permalink($prev->ID); ?>"><?php _e( 'Next Page', 'stag' ) ?> <i class="fa fa-chevron-right"></i></a>
        </div>
        <?php endif; ?>
    </div>
</nav>

I don’t know anything about php btw. I just guessed O_O”

I hope someone can help me!