In the first sentence this difference is more open even I can say the original sentence may be perfect tense like after they have paid. When they exited the vehicle, after paying the cab driver for their fare / after the paid the cab
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New2grammar
What is the difference between 'after having + verb' and ' after + verb+ing'?
When they exited the vehicle, after having paid the cab driver for their fare
let him out of the car some 500 yards away after having checked his papers
OR
When they exited the vehicle, after paying the cab drive