The number of expected reports would be determined by a combination of the total vaccinations and total deaths. There'd be a lot of reports of deaths that were not caused by the vaccine, but just coincidental in time.
Since kids get a lot of vaccinations these days, almost any death of a child should get reported, barring those caused by car accidents and other such obvious causes.
But you are not vaccinating against all deaths, you are vaccinating against contracting measles,in my example. To consider all deaths would be misleading as to the cause. And to say they died because they had the vaccine is misleading unless they in fact died from the vaccine. Having the vaccine and dying may be a coincidence It is a bit like saying all dead children had milk, so milk is somehow responsible. More to the point, the number of deaths from an ailment not vaccinated against is far, far higher than for those vaccinated no matter the cause of death of those vaccinated.
Certainly all deaths are reported, unless it is a kidnap murder.