In my experience, apps, airport screens, websites and the like are all generally fed from both the airports internal systems and also the airlines system.
Both of these are generally fed automatically by movement messages sent from departure airports, which can be questionable at best. It's not unusual for outstations to get the flight time wrong by +1/-1hr so if an incorrect movement is sent, everyone's expecting an aircraft to arrive (and subsequently depart) at the wrong time.
Of course these days with the likes of FR24 etc it's easier to see accurate arrivals time, but it depends how busy the airports/airlines ops department is to keep track of all the flights this way.
With the increasing use of ACARS MVT messages things seem to be getting better.