I actually prefer La Romana airport over Punta Cana myself.
Last time I flew into Punta Cana they weren't interested in you filling in your tourist card on arrival. I paid my $10 and went straight through immigration with just my passport and a blank tourist card. All they wanted was your money!!
I had flown there two months previously and someone had put me wise to it. Obviously I filled in the departure portion of the card before checking in for the return flight.