Two thoughts:
a) judging soley by that picture, both wheels look to be 17" or 18" I think 18" actually. Its just a weird angle, that may make some of the tire itself blend, and make you think they're different sizes. I might be wrong, but that's what I see.
b) When you 'upsize' your tires, on a MINI and most other cars you don't actually change the overall diameter or circumference of the tire. Instead, you get a bigger wheel, with a smaller sidewall, so the overall size stays the same. Sometimes the tread width increases, but you'd spec a size accordingly to keep the diameter the same. All of the MINI wheel sizes 15-18" have almost the same diameter, close enough to be within the error of the speedometer anyway. This is so called +1, +2 etc, sizing, depending on how many inches you increase the wheel size. With that in mind, I don't see how the DSC would care, except that the wheels would weigh a different amount, as tire + rubber don't weigh the same, which might affect it.
