The best answer I can come up with is that the Jubi left a small amount of its chakra within Obito before becoming the Shinju. Judging by how much chakra the Jubi possesses, it doesn't seem unusual that such a low amount can allow users to enter their Jinchuriki form, whilst the rest is still capable of functioning as intended for Infinite Tsyukomi.
That's just speculation though. It could be a plot hole, but we won't know for sure until Kishi reveals how exactly it works.