Near the end of 12 Monkeys, the terrorist mad man OPENED one of the vials of virus at the screening, so wouldn't that have initiated the collapse of society anyway, by starting the death of all who were in the airport at that time, and wouldn't that have traveled everywhere those travelers were going?
Because the plan was never to change the past but to obtain the original virus, as he told to Railly:
COLE: I just have to locate the virus in its original form before it mutates. So scientists can come back and study it and find a cure. So that those of us who survived can go back to the surface of the earth.
The issue was in current time virus was mutating and they needed the original form to craft a cure.
The goal of the scientists of the future was never to stop the outbreak (their past cannot be changed) it was to develop a cure.