All the manners in which the vaccine could have been tested, were employed before deployment. The only thing that wasn't done, as you note, is to wait for XX number of years to see long-term side effects. So in fact, we don't know what the effects of this vaccine will be in 10 years -- because the only way to know that is to wait 10 years. But... there is also no indication, from similar vaccines, that "something terrible" happens in 10 years.
A lot of people out there are just imagining, out of nowhere, than in 10 or 20 years, everyone who got the vaccine is gonna get autism or sprout a third nipple or keel over dead. But they're just imagining this. I can imagine a lot of things too... like, who here can prove to me that the new Doritos flavor introduced last year won't trigger brain cancer in 20 years? Anyone??