Your button code should link to the same website and not to a different website. That is the root of the problem. Once you fix that then there will no longer be a problem. The domain should be the same in the URL. If you are attempting to link from one site to another site then something is wrong somewhere. That is not how Mibew is designed to work and this creates a serious exploit/vulnerability on your website.
Example of Correct Mibew button code:
http://demo9.local/mibew/client.php?locale=en&url=http%3A//demo9.local/&referrer=http%3A//demo9.local/wp-admin/widgets.php
Also Aziz mentioned that the reason the button code is not working correctly could have something to do with Cloudflare. Your subdomain has a different IP address then your main domain. He said something looks wrong with your DNS information.