Remeber that the tailed beasts are like watered down versions of the 10T. Jigen used the 10T chakra to transform. When Naruto activated his chakra cloak it automatically activated on the ninja tech arm of kawaki and it allowed him to tranform for a split second.
I think it's more so that karma seals are connected to ototsuchi member which this one happened to be a juubi and jigen can absorb juubi chakra so he could absorb chakra equivalent to the nine tails
Yeah...that isn’t what happened at all
Idk why no one contested your theory but looking at those who agreed with it, I’m not surprised:
Naruto’s bijuu chakra was always activated, otherwise Kawaki wouldn’t have been able to move his arm. There wasn’t a spike of chakra from Naruto that caused Kawaki to transform because as you see in the spoiler, Naruto’s RSM activation did nothing to Kawaki:
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It wasn’t until after Jigen showed his aura that Kawaki underwent a partial transformation: