The main elevators in St. Anton am Arlberg are open until 16:00. Transportation in St. Anton am Arlberg is mainly represented by ski-buses, which run until about 17:30. If you plan to stay in St. Anton on apri-ski, you will have to take a cab. As in other Austrian resorts, cabs are best hailed by phone or taken at special parking lots.
It's unlikely that you'll be able to catch a car on the street, as this is not the custom here. You can leave a small gratuity for the cab driver, but it is not obligatory. It's easier to round up the amount on the meter to whatever is convenient.