Hi,
Please check your settings on the subscription tab of the Acymailing configuration.
In case you have disabled the unsubscribe page someone who unsubscribes is directed to the home page of your site where a confirmation will be shown in Joomla's System Message Container. I just checked your site and it does not contain this System Message Container. As a result no messages will be shown.
You can probably add it by changing a setting in your website's template. If you can't find it, please contact your template provider.
When you enable the unsubscrobe page you just see the nsubscribe form. To disaplay the unsubscribe form in your website's template you need to enable the parameter "Show the site's header".