To ensure that their mail that does come into your server gets routed to the Office 365 account, please take the following steps:
1. In System Admin > Manage > click on domain in question;
2. In the domain settings > Email set Inbound Message Delivery to External; use MX record if it points to O365; use host address if that's known (Microsoft uses a rotating IP so this may be difficult);
3. Ensure "Deliver locally if user exists" is disable, if you want ALL email to route onto O365.
Please let me know if this works for you.