Yes, the order is always the same. The refraction that happens in a rainbow isn't actually "splitting the light into colors," it's actually just taking white light (which is a combination of all the visible wavelengths of light) and spreading them out like an accordian. So, the colors you see will be ordered by the wavelengths of light.

Low frequency light wavelengths that we can see start at red and as the frequency increases you get up into orange, yellow, green, blue, etc.