None of the details in your calendar are published online. Only your availability, in the form of time slots, is published online. What’s more, since WhenWorks is an app that integrates directly with the Calendar app on your iOS device, it does not require you to provide your login credentials for syncing with the calendaring services you use (iCloud, GoogleCalendar, Exchange, Outlook, etc.).
Your sensitive login information used for accessing these services is NOT used or known by WhenWorks and is therefore not collected or stored in the app or online.