The "plainness" of Cistercian monastic reform and Calvinism (Puritanism being an English expression), relative to the situation the two movements were reacting against, looked different and had profoundly different theological roots.

Cistercian reform is ascetic. The idea was that the "decadence" or luxury of traditional monasticism, including/especially the Cluny-affiliated houses, was a distraction from focus on God. Early Cistercians sought to streamline their liturgy (chanted prayers), take up the burdens of manual labor for themselves, and flee from "the world" (engagement with lay people). They wanted less ornate churches, less ornate lives.

Calvinist reform is iconoclastic. They saw decadence not as distracting luxury but as idolatry! When Cistercian monks and nuns meditated on images of the Virgin Mary, Calvinists saw a danger that this use would slide into worship. Calvin himself went so far as to ban music from the churches of Geneva--completely antithetical to the Cistercian lifestyle that turned, fundamentally, on singing the Divine Office (appointed psalms) throughout the day, every day.

As you might imagine, Calvin's ban on music was often thwarted in Geneva, and conveniently forgotten elsewhere.