Unlike the mutants, who typically uncover their abilities during puberty, the Inhumans have almost always needed Terrigen Mists to transform them.
Likely, this is simply part of the ritual, as the actually process of Terrigenesis then occurs within containment chambers.
Hidden in their DNA is the potential for change, but the Mists and the Terrigen Crystals that create them are what allow Inhumans to truly unlock their potential.
The latest promo for Inhumans finally teases the process of Terrigenesis in the upcoming Marvel television series.