I'll take a stab...
If you are in one of the full auto modes then you need to change your mode to Av or manual mode. Tv also, but I rarely ever shoot in Tv.
To me if someone says "Dial down your exposure compensation",
what I hear is "You have too much
ambient light in the image causing either overexposure or motion blur from too slow a shutter speed."
Dialing in exposure comp. is done on the camera itself by adjusting shutter speed in Av.
In Av the camera gives you a starting shutter speed
it thinks will be best to properly expose the scene using
just ambient light. But you can adjust the shutter speed from that starting shutter speed...thus employing exposure compensation.
Making the shutter speed faster means you are "dialing down" the amount of ambient lighting squeaking in through the lens and hitting the sensor.
Same can be done in manual mode, however in manual you set shutter, f/stop, and ISO and the camera never gives you a starting point for a good ambient exposure like it does in Av or Tv. Thus everything adjusted in manual mode is essentially "exposure compensation".
The key with understanding exposure compensation is knowing what you are controlling. For me it is the control of
ambient/available light showing up in the final image.
Flash Exposure Compensation is simply making adjustments to your flash power in the available increments your strobe offers. You are controlling the output of the flash. Changes here won't have any effect on your shutter speed or how much ambient light strikes your sensor.
I think it is key to remember that whenever we use flash we are making
two exposures in one. An ambient or available light exposure combined with a flash exposure. All while the shutter remains open for a fixed amount of time allowing ALL the light to register on the sensor.
The first exposure captures the ambient light (maybe a lot, maybe nil, it's up to you) and starts as soon as the shutter opens and ends as soon as the shutter closes. The point here is you can decide how much ambient light reaches your sensor when in manual, Av or Tv. And when you do adjust it then you are doing exposure compensation.
The second exposure occurs when the flash goes off for a brief moment while the shutter is open and, ideally, exposes the subject properly. Any adjustments to the flash done here are flash exposure compensations.
Reviewing images on the LCD is helpful because you can look at how the light registered and make decisions on what to adjust or compensate for...ambient or flash light.
As for curtain sync...I don't know squat about the Inon strobe. So I don't know if you are referring to a setting on the strobe or a setting for curtain sync found in your camera.
If it is in your camera then it would only affect how your internal G9 flash fires. 1st curtain means it fires just as the shutter is opening. Rear curtain or second curtain sync means the flash fires just before the shutter closes.
Why does it matter? Well it goes back to what I mentioned earlier and having two exposures in one. "Ghosting" occurs when you have a flash going off in a scene that is also recording ambient light. If the ambient light is low and your shutter speed is slow enough to not freeze movement then your subjects movements may be picked up in each location they were when the ambient light was hitting them.
In first curtain sync the flash goes off essentially when the shutter is fully open. Thus the subject is well lit and frozen at the beginning of the ambient exposure. But as the burst of light from the flash fades the shutter is still open and still recording the ambient light hitting the subject. Every subsequent movement made by the subject after the blast of flash will continue to be recorded during the long shutter and show up as if they are semi-transparent...like a ghost.
Rear curtain sync would blast the subject with light from the flash right before the shutter closes, again freezing them clearly. In this way the ghosting would still be there but it would appear as if the semi-transparent "ghost" were trailing the subject rather than leading the subject.
I use rear curtain sync when I drag the shutter during receptions/dancing at weddings, when I want to blend in some ambient light with my flash.
Good Lord this response was long

...hope some of this made sense...

Keep asking questions, more experienced people than I will surely continue to help out!
Aloha,
Greg