I don't think McVay is completely changing his offense SoCal. This article certainly doesn't say he will be doing that. In fact, it can be inferred from several tidbits that it's still his offense.
First, McVay talks about a collaboration. That word alone implies he's learning some things from Stafford and Stafford is learning some things from him. Next, notice McVay's phrasing: "So you’re going to see SOME stuff that reflected in a lot of the success that he’s had in Detroit...." That tells me that McVay is going to implement things into his offense that Stafford has been good at.
Later the article refers to it being "McVay's offense" and notes that Stafford has to learn it. Don't worry! We're not turning into the Los Angeles Lions.