I assume you are setting up ADAL with AAD.
When creating AuthenticationContext:
Instead of https://login.windows.net/" + domainName (common)
Try
https://login.windows.net/[Guid for the web api configured on your client in Azure AD]/FederationMetadata/2007-06/FederationMetadata.xml
In its data store, Azure will now look for service namespace [guid] instead of what is deferred from the login name "billy"@timetray.onmicrosoft.com.
See in MSDN sample http://code.msdn.microsoft.com/AAL-Native-Application-to-fd648dcf#content
It states "Set the authority to https://login.windows.net/common to defer choosing the AAD domain till the user signs in."
Also, use http://www.nuget.org/packages/Microsoft.IdentityModel.Clients.ActiveDirectory/
I guess you also need to create users in Azure AD that are linked to existing Microsoft Accounts.