This has nothing to do with Amazon WorkSpaces, this is just how DNS works. You need to configure a hybrid setting to forward DNS queries to the authoritative DNS Server for the URL.
Amazon WorkSpaces are just Windows Desktops as a Service, joined to a Windows Active Directory. For Managed Microsoft AD, DNS is integrated into the Domain Controllers and can be managed through the RSAT snap-ins. It is the same way any Microsoft Windows AD with integrated DNS would be managed.
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