Dzogchen is the understanding that enlightenment can't be found outside a person
Not the best definition - most other schools would agree with this - doesn't make them Dzogchen.
Dzogchen (Dzog-pa Chen-po) means Ultimate Completeness or Great Perfection. Dzogchen is the understanding that everything is already perfect, everything is the way it is for objective reasons, the world at large is in balance, there is a great harmony behind everything whether we see it as good or bad. All so-called "problems" are just manifestations of higher-level principles at work, which by themselves are not problems. With this understanding, why look for Enlightenment? What other Nirvana do you need?
In what sense can we say that Buddha 'followed' the Dzogchen? The idea is, that after his Enlightenment, Buddha has awakened to the view of the Great Perfection. So his "internal state" (if we can speak of a state of a non-abiding Buddha) was not different from Dzogchen. But of course he understood that most people are driven by their emotions, attachments, illusions to a large degree - so they can't enjoy the Great Perfection as is. Therefore he taught them the path to clean their minds of the taints, until they get lucid enough that they can "awaken" (budd) to the Great Perfection.
The reason it's a separate tradition is because most Buddhists obsess over the path of purification - they can't seem to accept the simplicity of the result. So the various schools of Buddhism have evolved around the various practices of discipline, wisdom, and meditation. The schools that focus on the result are primarily Zen and Dzogchen.
But even Zen and Dzogchen agree that realization of completeness is not the end of story - this is only the right view - and then there is cultivation of the right view in practice of daily life.