Be sure that you are comparing the same flight. When you invoke FlightInfo/FlightInfoEx, the first result will typically be a flight up to 24 hours in the future. If you are specifying howMany=1 or only looking at the first result, then that may not necessarily be the one you want. You should ideally specify a howMany argument greater than 1.
In contrast, the FlightAware website will default to showing the most recently departed flight unless the next future flight is close to departure.
Additionally, 1576917900 is indeed 08:45 but only in UTC (specifically Dec 21 08:45:00 UTC 2019). I assume that flight is the one arriving in Amsterdam: https://fr.flightaware.com/live/flight/TFL377/history/20191220/2355Z/TNCC/EHAM which currently has an estimated arrival time of 09:55AM CET
When you are looking at the FlightAware website, times are normally converted into the timezone of the corresponding airport by default. I assume you were probably looking at this flight on our website arriving in Kralendijk https://fr.flightaware.com/live/flight/TFL377/history/20191220/1040Z/EHAM/TNCB which has an actual arrival time of 05:27PM AST