Through the use of Microsoft Graph, Timekit will be able to sync your on-premise Exchange Server's user's calendars and so provide online booking for your on-premise users.
To be able to connect and sync on-premise Microsoft Exchange accounts with Timekit you need to do three things in order for you on-premise server to be available through Microsoft Graph:
Be running Exchange Server 2016 CU3 and sync the on-premise Active Directory with Azure Active Directory.
Setup on-premise servers to allow Microsoft Graph to access auto-discover and REST API's endpoints.
Run the hybrid configuration wizard to get OAuth working.
Please also refer to this presentation by Microsoft, that goes more into details regarding how to setup the on-premise Exchange Server.
https://blogs.msdn.microsoft.com/deva/2017/07/22/use-microsoft-graph-api-to-reach-on-premises-cloud-users-of-hybrid-exchange-2016/
Once you've setup you on-premise Exchange Server, your users need to be created as Timekit resources. This is simply done by having them navigate to the link you'll find in the admin interface under "Onboard your users" as explained in our "Creating Microsoft synced resource" guide:
https://help.timekit.io/creating-microsoft-synced-resources