Minimalism from a technical writing and training perspective was first investigated and proposed in the late 1970s by John Carroll and colleagues at the IBM Watson Research Center. It has since evolved and been extended by a variety of stakeholders.
The link between DITA and minimalism (the IBM connection notwithstanding) is not exactly carved in stone but the two complement each other like macaroni and cheese. The macaroni (DITA) provides the infrastructure and model that you need to support the cheese sauce (the minimalist content).