The Site is pulled from the Designation for the Revenue from Payments, Events Registration Payments, Appeals, etc.
Note: The Site is assigned to the Designation from the Purpose it is associated with. If you change the Site on the Purpose, it will update the Site for the Designation.
With the use of Segment Mapping, you can configure a Site Segment Map to determine the Segment Value to assign to Revenue through the GL Distributions, which should display the Segment Value that is associated with a particular Site based on the Site assigned to the Designation.
When it comes to Events and Appeals, you can run into a situation where a portion of the payment has an associated Designation and a portion does not. In this situation, the Site would come from the Designation or show as "Not Used".