I've have an old release before upgrading Tasker to version 5.x. DutyManager version should match your android 4.4.2. See attached file.
The app doesn't have its own calendar. It rely indeed on any calendar found on the device. On my hand, I use to have a dedicated google calendar for our on-call account, synchronized and connected. It's easier to manage from our computer. But once again, it can be the local one on your phone.
And yes you have to make an appointment everyday for DutyManager to shift calls and sms. The keyword found in the calendar entry trigger the forwarding task.
I hope to clarify a bit how it works. Let me know.