Evil Kraig F (5/9/2013)
You have to RDC to the box, rt-click computer, manage, and check the services. Rt-click services and in properties for it you'll be able to see the login for it.
Usually jobs that run packages run under one of three contexts. The SQL Agent login, the SSIS service, or the proxy that's assigned to the job step. Your description sounds like it's the SSIS Service's login, so I was wondering if that matched what you were seeing.
If you don't have RDC rights and box admin, you won't be able to see the services and will need to inquire of those that do, probably the Senior DBAs on your staff.
You were right- the SSIS is running Under SSIS SERVICE - 'UserOne' (In our context) when I RDC-ed the box. Is this where i would make the change?