Yes. Ad zones and their tags are linked to the website they were created for, so they cannot be moved to another domain. If your website moves to a new domain, you need to:
Add the new domain in the Websites tab of your account and verify it.
Create new ad zones for the new website.
Place the new ad tags on the new domain.
If you only move to a subdomain of the same verified website (for example, from site.com to blog.site.com), you can keep using the same tags.
If you have any questions, you may contact our Support team via the email address support@monetag.com.