It isn't exactly truncated SHA-512 — that is, you can't compute a SHA-512/256 hash by computing a SHA-512 hash and then truncating it. Although the algorithm is the same as doing that, the initial state of the hash context is different.
(The same is true for SHA-224, which could be called SHA-256/224; it's a truncated SHA-256, but with a different internal state.)
(The same is true for SHA-224, which could be called SHA-256/224; it's a truncated SHA-256, but with a different internal state.)