Millennials are named after the turn of the millennium, while centennials are named after the turn of the century (not a hundredth anniversary). As a matter of logic, a turn of the millennium is, at the same time, also a turn of the century. The most recent instances of both took place at exactly the same time. One would thus expect millennials and centennials to be different terms for the same people. The distinction between them was manufactured by naming the millennials after the time when they reached adulthood or developed towards it, and naming the centennials after the approximate time when they were born. There is no deep reason for the naming to have been done that way; it could have been done the other way round.
Such terms are typically created and pushed into circulation by those who write for the popular media, and who are more interested in whether the term sounds attention-grabbing than in whether its use is conducive to clarity and precision. They have thus chosen 'centennials because it's a cool name, that references the already established name of millennials, not because it makes sense', as DJClayworth has earlier put it in the comments. Fortunately, at the moment, the term centennials does not yet seem to be well entrenched; those of us who do care about clarity and precision can thus still hope that it will eventually fizzle out and be replaced by something else. Generation Z may be unimaginative, but it does have the advantage of not being confusing.