Hello
using Windows Azure to host AD domain (and other services) is exactly the same than running these on your on premises
if you Azure Active Directory domain is standalone - meaning not connected with your on premises domain, you have to setup a Directory Synchronization to synch your AD users to Office 365
For SSO, you have 2 choices: install and configure ADFS or use the new password synch for the dirsycn tool
for both ADFS and Dirsync with password synch, you have to update the UPN (@domain) to an internet domain associated with Office 365 (such as @microsoft.com) instead of the @domain.local you may have which is attached your internal domain