Hi Customer,
The behavior you encountered makes sense.
If you have an on-premise Exchange system, please mail enable them via the Exchange management tools, such as the Exchange Management Console (EMC).
If you don’t have an on-premise Exchange system, you can refer to the following article create the security group on Office 365 side directly. If you use this way, you can manage it on Office 365 directly in the future.
http://technet.microsoft.com/en-us/library/bb123521(v=exchg.150).aspx
Thanks,
Claud