I Believe the stripes on ashura's cloak and the general design of it is from his power that he awakened. Possibly the entire creature.
Lets say that were true
Naruto being his reincarnation,
I believe when naruto awakened bijuu mode (when he got the stripes)
It also triggered the resemblance (him being ashuras reincarnation)
All the chakra and power of kurama being exerted through narutos body makes hid body think its his and starts triggering the resemblance
I also believe narutos will gain a similar creature to ashuras and it could mix with his bijuu mode/transformation
Lets say that were true
Naruto being his reincarnation,
I believe when naruto awakened bijuu mode (when he got the stripes)
It also triggered the resemblance (him being ashuras reincarnation)
All the chakra and power of kurama being exerted through narutos body makes hid body think its his and starts triggering the resemblance
I also believe narutos will gain a similar creature to ashuras and it could mix with his bijuu mode/transformation