I do it the same way, Developing for desktops and then going down for mobiles.
In my opinion, going mobile first can make your development process desktop second
Don't get me wrong here, I do believe that mobile first approach is great and solves a lot of problems and the response by @xirclebox is also pretty accurate here but I also believe that desktop web has a lot of potential and by focusing more on mobiles, when we "expand" our design, we tend to ignore that potential.
This said, I think would still say that mobile first is pretty great if you have the right content and design for it. But if the content demands it, go desktop first!