Ok, let me get the answer! Here, every path and resources for every way to get you started. Your scenario is not clear to me, so I will try to be common.
There are four ways to update live tiles in Windows 8! And this is true for the primary tile of the application and subsequent secondary tiles created by the application.
1> Firstly, the application can update the tile during operation
But you asked how to update when it is not running:
2> The user can deploy a background task using his Windows 8 application. This background task runs periodically and can update the application tile while it is running. The minimum frequency of background tasks is 15 minutes. Windows 8 allocates 1 processor for every two hours to complete a task. Your task can be performed as often as you want, until you exhaust the selection.
3> At startup, the application can open the WNS ( Windows Notification Services ) channel. When it is not running, the web service can trigger tile updates in WNS.
4> A tile can be configured to pull from a URL . The XML from this URL is periodically evaluated for deltas, and the tile is updated when it is detected. Tiles expire by default after three days.
Clarification point : you cannot call something like a tile update when the OS boots. Firstly, in Windows 8, the idea of rebooting (or at least closing) is practically not recommended. But your Store application can only run in the ways mentioned above, and cannot do something like the StartUp folder (in the past) or RegEdit / Run (in the past) only. But service or timer triggers are approaching you.
And that is the answer. Good luck dude!