Why Kaga might not receive warning in time

Would Kaga have been warned about the Tsingtao escalation?

Possibly not, because Japanese command districts did not always pass urgent information laterally or distribute it reliably from higher headquarters.

Separate command districts and weak information distribution could leave Kaga unaware of events elsewhere. Messages were supposed to travel upward and then be redistributed across the command structure rather than pass directly between neighbouring formations. Sometimes that redistribution happened and sometimes it did not. The same weakness later left officers making plans with ships that had moved, changed tasking, or already been lost. The scenario therefore depends on a documented command-and-control vulnerability rather than on the carrier simply ignoring a clear warning.