When you create an airport and Sims come to your city, where do they come from? Existing cities from other players, other cities in your game, do they just pop up?
In the tutorial when the game starts. They explain that the airport is used to move workers from one city space to another. There is a way in the region view to see the flight paths of airplanes between each city.
I think you must have at least 2 cities in the region, each with an airport to have workers fly between cities.
If you have another player in your region, ask them to make an airport so you can share workers.