WhenWorks queries the Calendar app on your iOS device periodically to check your availability. This happens in the background when the OS wakes up the WhenWorks app during Background App Refresh, approximately 2 or 3 times per hour.
In addition, the app will receive silent push notifications from the server, waking it up periodically to sync its availability, as well as immediate push notifications if a meeting is created online so that the meeting is added to your device right away.
It's important that you NOT force quit WhenWorks as that will stop it from running in the background to monitor your availability and stop it from receiving silent push notifications from the server when meetings are created.
If you want to force a refresh, you can launch WhenWorks on your iOS device. That will cause the WhenWorks app on your iOS device to pull your latest free/busy status from Apple Calendar and upload your availability to your WhenWorks scheduling page.
Then make sure you just exit the app normally by switching to a different app without force quitting it. That will ensure it continues to run in the background during Background App Refresh and will continue to receive silent push notifications.