Don't drive it before getting some water poured into the coolant recovery/expansion tank (just to the right of the radiator).
Sounds like there was coolant leaking from the drain plug on the upper passenger side of the engine block.
Dripping onto the hot exhaust caused the excessive steam/smoke, well before the low coolant light triggered.
No harm done - fortunate it happened just when you were parking it.
If water added does not immediately leak out, probably O.K. to drive out of the airport.
Watch temp. gauge carefully.
A yellow low coolant light is just a caution, red light should stop immediately (or avoid getting to that point).
Could be unrelated to the $800 service if a hose has gone, or some other part of the cooling system.
But let them talk their way out of it. Good luck.