Classy, I based my explanation on the terrestrial set up, but the same conditions apply to a satellite system, it is just that the distribution path is slightly longer. However, it is not the length of the path in this case that introduces the noticeable delay, but the electronics and signal processing at stages along the way.
Consider the geostationary tv satellite high above our heads. To be geostationary (appear in the same place in the sky all the time) it has to exactly match the rotation of the earth. To do this using momentum and an equilibrium of forces requires the satellite to be 35,900 kilometres above the surface, so the signal from the earth to the satellite and back will be at least twice that, i.e. 71,800 kilometres. As the signal path will be unlikely to be exactly perpendicular to the Earth's surface, the path will be slightly longer than this, say in the order of 75,000 kilometres (very generous). The radio signal travels at a speed of 299,792.458 kilometres per second which for ease of calculation we will round to 300,000 kilometres per second. So the time taken for the radio signal to go to the satellite and back is 75,000 divided by 300,000 = 0.25 seconds.
A quarter of a second is hardly enough to be noticeable.
Electricity travels somewhat more slowly along solid cables so the delay is greater per kilometre, but the distances are considerably shorter. When chatting on the telephone to Australia in the days before satellites, and the signals were sent on cables for most of the trip, I noticed the delay appeared to be about 0.8 second for the 38,400 kilometre round trip.(average signal speed through cable and electronics on the way then being 30,720 kilometres per second)
The delay observed in the tv example by Martinf57 is almost wholly due to the electronic processing of the signal, and most of that is the multiplexing just prior to the main transmitter.