Yes as Joe mentioned when the float needle isn't shutting off in the carby the fuel level gets too high and starts to leak out the primer orifice and into the remote primer.
The problem with this type of mower if you were to change the carby cap to a later model with the primer on the cap ,it would be too difficult to prime as there isn't a lot of room to get your hand to that side of the carby.
I would buy a metal needle and see if that fixes the leak also every old Victa I've had problems with the rubber remote primer ,the problem was the rubber primer had aged too much and the rubber had gone hard ,so you may be interested in a replacement primer for easier priming.