That will happen if the link doesn’t include http:// in it. For example, if the user has entered just linkedin.com into the field. In that case <a href="https://wordpress.stackexchange.com/questions/284064/linkedin.com"> will be treated as a relative link by the browser.
Use esc_url on output to ensure a full valid URL with protocol is output:
<?php echo esc_url( $directors['linkedin'] ); ?>
PS: The URL field in ACF, rather than just a text field, has validation that would help with this.