Zhiyi is famous as the first Chinese Buddhist master to truly break from the Indian Buddhist tradition (= not just following a school of Buddhism already established in India).
This school was entirely Chinese in origin, rather than a transplantation from India. Inasmuch as the name is taken from a Chinese mountain, we can see that it was intended to be a truly Chinese Buddhist school.
This school of Buddhism is also known as “The Lotus School” because of the importance it gives to the Lotus Sutra.