Permalink misbehaving in Custom Post Types

The rewrite argument of register_post_type() will help you with this. The rewrite argument is an array of different arguments, the one you’ll need is with_front, which desides whether the permalink base is prepended to your post type. It defaults to true, setting it to false will not include the permalink structure in the permalink. It would look something like this:

function do_careers() {
 register_post_type('Careers', array(
    'labels' => array(
        'name' => 'Careers',
        'singular_name' => 'Career',
        'add_new_item' => 'Add New Career',
        'edit_item' => 'Edit Career',
    ),
    'description' => 'Careers',
    'public' => true,
    'menu_position' => 20,
    'supports' => array('title'),
    'rewrite' => array(
        'with_front' => false,
    ),
 ));
}

add_action('init', 'do_careers');

You can also add a slug argument to the rewrite array to make the post type slug different from the post type name, if you wish to do so.