Adverse reactions to medication are not rare. I reacted adversely to aspirin when a teenager....
"In the US, 3 to 7% of all hospitalizations are due to adverse drug reactions."
SOURCEImportantly
side effects are not
adverse reactions. I was on a medicine that had a sticker on the bottle that warned MAY CAUSE DIZZINESS - and it did for me, but it does not for everyone.
The vaccines have side effects for some people, this is a known, and expected result. In any population there will be people who will have an unexpected reaction to any medication whatsoever. But if people started spontaneously speaking Dutch or their skin started to develop a rash two weeks after the vaccine - and that was not a known and expected side effect - then we'd be into "adverse effects" territory, and even then, it's not a dangerous adverse effect.
The link below is worth a read - in short, an "adverse reaction" is
anything that was unintended from a headache to death and the overwhelming majority of people do not have them because of the clinical trials and testing that go into the development of medicine.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6297296/