Since DAU in ZCM is hard-coded to once every 24/hours, when exactly does it run?

Meaning like:

Let's say some time on Monday, it ran on my pc
On tuesday, pc was OFF
On Wed, I come in and power on PC and login.

When does the DAU run? Does it base it upon the device refresh schedule in the Zone? So if I have things the DEFAULT, it would be some random time AFTER 300-600 seconds AFTER I power up the PC?

Or is it even more random and it's some random time when the PC is on?