No I don't think so. We didn't see 1st or 2nd hokage or Oro's hands for that matter, come out of Hiruzen. They came out of the Death Reaper. We didn't see Kurama's chakra leave the Death Reaper either. So I believe it's still there, and Oro could only let the things he wanted out of it, and since he didn't know about the yin part of the chakra, he didn't release it.
Then what is Minato's present, you might ask:
It's something very personal, and very important to Minato, that he always wanted to give his son, perhaps when he grew older. This is normal for any father to have such a thing, that was important to him. My best guess is his first head band or something like that, which Minato would have wanted to give Naruto, when he became a Genin. But it could also be something else!