The crux: just because a vaccinated person can shed a disease doesn’t mean that the unvaccinated population is not responsible for community outbreaks.
Here’s why:
Transmission levels in a community are measured by R0 (“R naught”), which represents the average number of transmissions per case of any disease.
No vaccination is bullet-proof. We intend them to reduce the number of transmissions caused by the vaccinated individual. Even though vaccinated individuals shed mumps, they shed it less than their unvaccinated counterparts (source).
If we really consider this, though, it’s obvious. If the vaccinated got and transmitted mumps as though they were not vaccinated, unvaccinated individuals would get mumps at the same rate, regardless of outbreaks, because everyone around them would be getting it and passing it as though the vaccine didn’t exist. Of course, this isn’t what happens because the vaccine successfully reduces R0 and reduces it to under 1 (the minimum requirement for ongoing community spread) when the population has a healthy vaccination rate.