Your rule triggers are for ‘changed’. They will fire for any state change, no matter what the source was. That’s the way they are designed to work.
openHAB is multithreaded, so things can and do happen in parallel.
Your rule DaikinPowerUpdate is triggered by a change in DaikinPower and issues an update to vDaikinPower. That goes onto OH event bus.
Meantime the rule goes on to display the state of vDaikinPower, which is still OFF.
A short time later, OH actions the update, generating the change to trigger the other rule.
This is all working as expected. Commonds and postUpdates are asynchronous, never wait before carrying on, never produce instant results.