GeoTIFF files don't have to represent RGB colour images. They are general data-storage rasters, and bands can contain any numerical values, including decimals, negative numbers, things bigger than 255, bigger than 10,000,000, smaller than -9999 and so on. A band could be altitude in metres.
If this file is supposed to be interpreted as an RGB image then it may be a high dynamic range RGB image, with maybe 16 bits per channel. You'll have to check the documentation for that, and then set the min/max for each of the three channels corresponding to the colours.
The scale of 0 to 255 is a common convention because 0 to 255 can be encoded in 8 binary bits which packs nicely into a byte. But that only leaves you 256 shades of each colour which might not be fine enough for some applications.