I don't think we need to know right off the bat, but there should definitely be a legitimate in-universe reason, even if we don't know what it is for most of the film. In fact, they probably won't even know themselves. But there must be an eventual explanation of some sort, at least hinted at. I think they could still be genetically engineered (by a villain?), without being mutants, since "mutant" implies random mutation, while genetic engineering is a deliberate process.
And I kinda hope they aren't tied to SHIELD, or even know about them at first. Depending on how much they use their powers, its entirely possible that SHIELD isn't aware of their existence yet either. This makes them sort of a rogue, unknown element, as well as a sort of everyman, or audience surrogate. Their interactions with the Avengers might stem from them seeing the public footage of the attack on NYC, and realizing they aren't as unique as they thought.