This is the question people actually want answered before they book an airport pickup, and it rarely gets a straight answer.
The pickup moves with the flight
An airport booking carries your flight number. The arrival time is read from the live flight, not from the time you typed when booking. A three-hour delay moves the pickup three hours; nobody has to call anyone.
Waiting time is included, within reason
Domestic arrivals include 60 minutes of complimentary waiting from the moment the aircraft is on the ground. International includes 75, because immigration is genuinely unpredictable. City pickups include 30.
What flight tracking does not fix
A cancelled flight rebooked onto another. The system is watching the flight number you gave it. If you are moved to a different flight, the booking needs the new number — call dispatch and it takes a minute.
A diversion to another airport. If you land at Ontario instead of LAX, that is a different journey at a different price. It can be arranged, but not silently.
Baggage that takes two hours. Past the included window, waiting is chargeable, because by then the car and the chauffeur have been held for another trip.