There is no separate data kept just for the customers. What you see in the app is from the data used internally by all the employees who are working to service and operate the flight.

When you see things that are obviously wrong, it is because they haven't yet decided what they are going to do to fix it.

The default is for the departure time to auto-update based on the status of the inbound aircraft. When that is changing frequently, such as an inbound aircraft that is stuck on the ground elsewhere with an ATC or Mx delay, the automated system will see the excessive number of updates and will recommend to the controller in station or network operations control to turn off the auto-updating. When that happens, it's up to SOC/NOC controllers to keep it updated.

The FAA flight plan data is separate. The flight plan is filed with an estimated departure time set as the scheduled departure time. If a delay is internal that time is good from 30 minutes before until two-hours after the filed time without being updated. If there are ATC delays, it's up to the flow control system to update though the larger airlines can swap their slots around between flights in order to minimize the impact of the delays.