it is my theory that it has mostly to do with Naruto and Minato. when kirin talks about naruto's chakra she says it is bright warm and orange she doesn't say that kurama's chakra is bright warm and orange this leads me to believe the appearance of there chakra cloaks has to do with them more so than kurama
we know that Naruto when he goes into tailed beast cloak he does so by absorbing kurama's chakra which looks blue when he absorbs it he then transmogrifies the chakra so that it fits his chakra signature so it is my theory that when he enters tailed beast cloak he simply absorbs kurama's chakra and transmogrifies it so it matches his signature as such its appearance is that color and what not because Naruto absorbs it into his actual normal chakra reserve and as such what we are seeing is naruto's chakra enhanced by tailed beast chakra and since minato is naruto's father there chakra signatures are similar and as such they have a similar tailed beast cloak