No, they only need to be independent of reality, reality in this case doesn't mean universe, multi verse or whatnot, reality refers to what they govern which in the case of the source is its individual.
The source isn't affected by the destruction of the person but destroying the source would completely destroy the person. The source also encompasses the past, present and future of the person.
This is typical type 1 right here so I don't know why the source is only regardless as type 2 concept.
Also, all orders are type 1 concepts. Destroying any order would destroy what it governs and this destroy the world but of you destroy what the order governs nothing happens to it.
For example NAFTA is the future god. In their fight, Anos destroyed all future possibilities yet nothing happened to the order of the future. The reality the order of the future governs isn't the entire world, just the possible futures.
For the god of traces as well. Anos destroyed not only the world of traces but all traces of the past as well yet the order itself was unacceptable.
Basically both the source and all gods orders are type 1 concepts