It was very over exaggerated in the movie. The effect is real. There's time dilation due to both special relativity (the speed of satellite) and general relativity (how deep in the gravity well the satellite is).

The time dilation in the movie is so extreme, that I'm not sure a planet could even exist so close to the event horizon. There is such thing as innermost stable orbit around black hole; I wouldn't be surprised if for such extreme time dilation, a planet would need to orbit closer than innermost stable orbit (which would be impossible).

The clocks are slowed down by orbital speed, and also slowed down by how "deep" in gravity well they are. This means anything in orbit will experience its clock slowed down depending how fast it moves. Further away, the slower it moves, the less the clock in the satellite is slowed down compared to the surface of the body it orbits. However, the further away the satellite is, higher in the gravity well it is, and faster its clock ticks compared to the clock on the surface of the body it orbits. In case of Earth, there is an orbit where these two effects cancel each other. See this graph https://en.wikipedia.org/wiki/Gravitational_time_dilation#/media/File:Orbit_times.svg