Does your plot look like this one? The average number of electrons emitted by a dynode is linearly proportional to the potential difference between dynodes. This means that if one were to double the voltage between two dynodes, the average number of secondary emission electrons from that stage would double as well. In fact, fitting a straight line to the data we collected yield a slope of 0.025. For this particular photomultiplier tube, the average number of secondary electrons emitted per incident electron is equal to 0.025*(voltage between dynodes).
Suppose you had a photomultiplier tube with several stages. If you double the voltage between each dynode, each incident electron would eject double the number of secondary electrons, but would the total number of electrons after several stages be doubled as well?