I'm not sure if I understand the question... but let me try.
On Mixer panel, imagine Panel and Style section as some sort of "pre-amplifier" settings, where the goal is, to get various voices/instruments in balance with each other: background organ maybe a little quieter, solo guitar a little louder (than organ), snare just loud enough so rhythm can be heard, etc. -that is, you make volume ratio between used instrument. Similarly, you also "position" instruments "on stage", by using pan settings.
Now imagine Compressor on Mixer Panel as (final) amplifier, into which "the whole band" is connected. Means, here you decide about final sound of complete band. Why is that needed? Because when you create your "band", you are trying to make them sound perfectly balanced. However, you never know how the "band" will sound in particular room (where you will perform). It can happen, that even everything was nice at home, that's maybe not the case at another place. Let's say, there's too much bass in room.. or you wish to increase total volume, without increasing low frequencies too much. Of course you don't wish to decrease volume of bass guitar (and drum) in every style you will use. And that's where you use Compressor/EQ -by using it, you define how the "band" will sound in particular room (without changing voice and style parameters).
Compressor/EQ settings do (obviously) affect both, MAIN & SUB OUTPUT on keyboard back panel. The problem is (or can be), MAIN OUTPUT is also affected by Master Volume knob on top panel -but SUB OUTPUT is not! That is, by using Master Volume knob, you only change volume on MAIN OUTPUT (and for built-in speakers, of course).
Speaking for me, I really don't understand why Yamaha did that. In my opinion,
both outputs (MAIN & SUB) should only be influenced by Compressor Output setting. Or: there should be a choice where user could decide what he prefer.
I hope that somewhat answered your question
Bogdan