i would get an uber if i were you. check the time approx it takes when you're at the first stop(tsing yi), then time it accordingly(I usually allocate 3 minutes from train to the drop off area where uber picks up pax... add a minute or 2 if you have many bags or kids - so start looking for cabs before you get of the train if its showing 10+ mins, or before the lift if less). I'd assume you have bought a ticket before you get on the train anyways.
Uber would save you luggage surcharge which is payable on a taxi.
Im not surprised, i got scammed when i last took a taxi from the airport. They are in general a terrible bunch (if not scamming, bad driving.)