Hi, may I know what's the difference between Vi's "You May exhaust me" to this context of emperor dias?

The may is identical and means that the trigger is optional to put on the chain. The difference is Vi's "exhaust me to [do X]". This makes it a cost to be paid on finalization, in comparison to "[do X]. If you do, do [do Y]" which happens on resolution because it's not a cost in game terms