Your href is empty. Let's have a look at your source code:
<a class="alt-caption external" href="http://">www.aimassociates.nl</a>
The href attribute is looking at "http://".
Maybe you must add an echo?
<?php echo the_field('url_site'); ?>
It's weird that the same PHP code returns different result, have you copy/paste the code just as is in your files?
Why don't you try this?
<?php $site_url = the_field('url_site'); ?>
<a class="alt-caption" href="http://<?php echo $site_url; ?>"><?php echo $site_url; ?></a>