I have found opinion divided between use of throttle pumping and primer to prime, however, there appears to be more risk of causing fires with throttle pumping - particularly if the carb is upside down on the bottom of the engine - where does the fuel go? Some A/c however do not have a primer, and the POH specifies throttle pumping (robin)
The primer is designed for the job.. and usually deposits the fuel in the induction manifold, directly upstream of the cylinders. It's operation is independant of the throttle, it's just a sliding pump that chucks a slug of fuel.. This may account for different instructions - different size of priming pump?