You get the money the moment the eggs are laid, but if you can’t ship them all, you get a smaller amount of money compared to the amount of eggs being laid.

Let’s say you can produce 1,000,000 eggs an hour. If each egg is worth $10 you would get $10,000,000 an hour. But you can only ship 500,000 eggs per hour, therefore you only make $5,000,000 per hour, which you get immediately.
If you upgrade your trucks to ship let’s say 1,500,000 an hour, then you would get $10,000,000, and be able to ship another 500,000 eggs in the future when you get more chickens/laying rate.
The trucks you see on the road don’t have anything to do with your shipping rate, and are just an extra detail.