In the DC comics, people who get powers posses a "metagene", a chromosomal anomaly that allows them to (potentially) survive great danger by rapidly developing abilities which either allow them to survive the dangerous event, or in the case of energy-based events, absorb or metabolize the energy.
It's not a guarantee that having the metagene will cause one to obtain powers, as one may never be exposed to a dangerous enough event to trigger it. Similarly, several people exposed to the same danger may exhibit different powers afterwards.
The explosion of Wells' accelerator is an example of I refer to as a "white event" - a large event that provides the impetus for many people to spontaneously exhibit powers in a comic book world. It's the general source of the energy required to trigger the metagene, but as explained, would affects different people differently.
While the metagene has no been explicitly mentioned on the show, it may still be a concept in play.