We don't really know where their Rikudou power is stored. It's more or less a part of them, it's probably different from the Kyuubi's chakra that comes from inside of Naruto, but is a separate being.
Though Rikudou chakra itself is more or less attached to them in a way where it can't be removed (My guess). Which is why they were capable of progressing so fast between receiving the powers, and the Last/Boruto Movie. EX - Sasuke destroying a meteor with Chidori, and Naruto crushing a large part of the Moon's surface with a kyuubi enhanced fist.
It wouldn't make much sense for it to be a completely separate form of pool away from theirs, it might be like the seal Minato created for Naruto, which blend his chakra with Kurama's. So in a sense it's there own power?
This is all just a theory though. Don't take any of this seriously :lol