When you navigate to an invalid page on the primary domain (pages.domain.com/invalid-page.html,) you will be redirected to the Fallback Page: www.domain.com.
If you were to navigate to an invalid page on the Alias (such as pages.otherdomain.com/invalid-page.html), you will be still be redirected to the Admin Settings Fallback Page: www.domain.com.
The Domain Alias Settings are particular in the sense that the exact setting is for the "default page". You will only be redirected to the Domain Alias Default Page if you were to navigate to pages.otherdomain.com.