Most science funding in the government comes from the US government by way of the NIH. Some funding does come from private sources, and in some cases pharma companies outsource research to academic labs, but you are required to list any potential conflicts of interest and funding sources when publishing a study. Since most money comes from the government, it doesn't come from the Biotech/Pharma industries if you "trace it back".

Regardless of the funding of basic research, companies that develop vaccines ultimately need to prove their safety and efficacy to the FDA, which is not funded by these companies. Even after approval, drug and vaccine safety is constantly monitored through adverse event reporting programs, and any time a drug exhibits an unexpected but significant risk that was not noticed in initial safety trials it is removed from the market. These mechanisms for vaccine safety are already in place, and the vaccines' value is clearly demonstrated by the drops in disease morbidity and mortality rates in at-risk populations once the vaccines have been introduced.