get_next_post set the category

Try this:

$the_cat="latest";
$term_args = array('orderby' => 'term_id', 'order' => 'ASC', 'fields' => array('term_id', 'slug'));
$terms = wp_get_post_terms( $post->ID, 'category', $term_args );
foreach($terms as $term){
    if($term->slug !== $the_cat){
        $terms_to_exclude .= $term->term_id.',';
    }
}
$next_post = get_next_post($in_same_term = true, $excluded_terms = $terms_to_exclude, $taxonomy = 'category');