If you have had an oxytocic drug (used for third stage) usually given in the leg then yes they do "pull on the cord" its called CCT or controlled cord traction, this is done after signs of seperation are sign ie. a gush of blood, you also palpate the abdomen to ensure she is contracting otherwise you should leave alone.
However if you had a physiological 3rd stage (no injection) then NO they should not have pulled on the cord, they should let it be, put the baby to the breast and watchful waiting until you probably feel the urge to birth it yourself then they just catch it in the lovely kidney dish lol