I worked at Publix for about a year and made the buttercream more than I want to remember! Good news/bad news.
Bad news: The buttercream comes in a mix-- it's like a giant block of almost fondant-like stuff, consistency-wise. You soften it up and then add regular unsalted butter and some water (from a weird water hose machine-- I know that isn't relevant, but that thing always seemed strange to me so I just had to mention it
Good news: It shouldn't be too hard to replicate, or at least come close to. I read the ingredients for the buttercream mix blocks on more than one occasion to try and pick them apart, and never found anything out of the ordinary. It basically came down to vanilla flavoring, egg whites, and powdered sugar. I've never really tried to replicate the buttercream, but if I recall that really was all those blocks were made of.
If anything I guess there'd be some unusual flavoring they use. But I can confirm that much: egg whites, confectioner's sugar, vanilla, unsalted butter, water.
Sorry I couldn't be of more help.