An Amasty extension is not domain-related, but installation-related. If you run each website on a separate production Magento installation, you need a separate license for each of them. However, if you run several domains on the same instance of Magento, you can use one extension license. You don't need separate licenses for any mirror, staging, or developer versions of your Magento installation either.
Thus, our license agreement allows using one and the same extension license for one live (production) Magento installation and all dev/mirror/staging instances. Consequently, when carrying out License Registration process, separate registration projects need to be created only for live (production) instances. All dev/mirror/staging instances are associated with corresponding live (production) environments.