There are no tolls going into the airport, they shouldn't be charging you anything for that. You do have to pay the outgoing tolls (unless you take the back way). Technically, a non-Boston cabbie is supposed to go to the Massport office and pay the airport surcharge, then pick you up, but that doesn't happen.

As an ex-cabbie, not only do I always call Green to pick me up at the airport, I always tell friends to wait for me on the upper deck and I pick them up there. Picking-up on the pick-up level is for suckers!