It's all a little sticky. First of, it's best to split the narutoverse into 4 parts:
- The Impure World - world of the living,
- The Pure World - world of the souls/dead,
- the world in between those - this is where the conversation between Kakashi and his father took place, you need to cross this world to reach the pure one. Seemingly, Nagato's Rine Tensei works best when souls are still here, otherwise it would be impossible to revive so many people at the same time,
- all other pocket dimensions and the like (including DG's belly).
Chakra is a combination of Soul/Mind and Body/Life/Physical Energy (you can also add Natural Energy to it ), thus each portion of chakra posses a copy of the user's mind. Usually, the copy of the mind disappears when the energy is used up. There are a few exceptions, like the Kage Bunshin, that somehow allows for the copy of the mind to return to the user, allowing it to combine the experiences of both. It's also possible to combine and retrieve the chakra (thus the copy of the mind) stored within other objects or even human, as we have seen it done by Orochimaru. It's worth noting that leaving a bit of one's chakra, is the same as that part of the person remaining within the Impure World, even if that person technically died.
Now let's look at other elemental jutsu that control terrain, for example one that creates water vortex. By controlling it with your chakra, you are basically controlling it through your mind and energy that you input into it, in a way you could say that the water gains your consciousness. The question is what happens with it after the energy is used ? It certainly doesn't return to the user, but there isn't any need for it to go to Pure World as well. It likely disperse within the nature, perhaps even joining with the natural energy that flows around (especially since the GM to Jyubi transformation proved that Chakra can be completely transformed into Natural Energy).
Now we need to consider one more thing, that Humans (and perhaps other beings in narutoverse) seem to posses a kind of Soul Core, especially apparent when one of the Pain's paths takes out a soul by taking the core, rather than simply sucking mind energy. It's likely that the thing that goes to the Pure world is not mind energy itself (that likely stays within the Impure world and later combines with Natural energy as a natural process ?), but mainly the core. This would mean that if a part of the core isn't with the amount of Mind or Chakra left in the Impure world, then it would not go to pure world by itself. Thus, the part of chakra (thus mind) that was left within Naruto never reached Kushina or Minato. That is if it is the way I explained it, because unless it is directly stated by Kishi, it's hard to confirm anything anyway .
Oh right, the fact that the Death God have sucked a part of Oro's Soul Core, which was linked to his arms, proves what I said above, because he still couldn't regain it's proper use even by over taking other's body or mind energy.