The “constant gain” button prevents the illusion of making you think that what you are doing is better when in reality it is only louder. With this activated, the leveller effectively reduces the input to match the output - in short, it keeps your perceived volume the same. Normally limiting down by 2dB will boost the apparent (or perceived) volume by almost a third (an increase in gain of 6dB is effectively doubling the level) and the result will always appear to sound better at first simply because it is louder.
With this button active the trap is avoided as the plugin will compensate your increase in output level by reducing the input - it is the same thing as a constant gain EQ (112dB’s Redline equalizer is a good example of this). I really recommend reading the manual - not only is this explained in detail, but there are some good tips to help get started with it.
FG-X is a mastering tool not a mixdown buss compressor so designed to deliberately not add “colour” in the way you mean, as that is not what mastering is about. Mastering is the process of preparing a completed, approved mix for it’s intended release media and not part of the mix process - mastering tools are generally designed for transparency & accuracy, not colour.