It depends if you are shooting jpg or raw. If you are shooting raw, the image that is shown on the LCD of the camera is just the jpg contained within the raw: but when you open it with a raw capable editor you still have room for setting the white balance. You still have to interpret the value of the raw data pixels and white balance is simply establishing what is to be interpreted as a 18% gray.
If you shoot with a jpg, this interpretation is made by the camera when you are shooting: you don't have the raw data any more but you have a finished image and you lose the latitude to decide what is gray.
DSLR always give you the chance to record your photo in raw format. By the way, often when you open the raw file, which is usually rather large, you see a flashy image, which disappears when the raw is loaded and is often replaced by a duller image. This is because the first image is the (already developed) thumbnail jpg within the raw, with a bit of processing already applied (saturation, contrast, whatever). The "dull" version is waiting for you to be processed.
On the contrary, the iPhone typically doesn't allow for raw shooting, so you are "stuck" with the jpg that it has produced. You can check this link for a possible approach.