Why didn't Naruto's Rasengan turn red when he got Kurama's one-tailed cloak against Sasuke?
While reviewing the fight scene, I'd like to point out something that I noticed.

Towards the beginning of Naruto and Sasuke's battle, Naruto's Rasengan was its normal blue color, as shown here. This occurrence was prior to Naruto gaining the 9 Tails Cloak.



Towards the end of the battle, while Naruto's Rasengan was forming, I noticed that this ones color was actually more of a purple color than the normal blue (albeit not red either). This is shown here



Purple is a combination of the colors Blue and Red. So with that information, we can deduce that the chakra used to perform Naruto's final Rasengan was a mixture of Naruto's blue chakra and Kurama's red chakra.