Exposure compensation changes the METERING that the camera will use.
In other words, suppose you're using "Program" mode and you set the compensation to -2 but the camera is allowed to set aperture, shutter, and ISO. If the shot metered for, say, ISO 1600, 1/125th, and f/4, then "-2" says to shoot at TWO full stops below whatever the meter reads. So it might actually shoot at ISO 400, 1/125th, and f/4 (assuming it was allowed to change the ISO.)
You could turn off auto-ISO so that the camera cannot alter the ISO you set and can only play with f-stop and shutter speed.
If you want to force the camera, you could turn off auto-ISO, and use, say, shutter priority. This would force the camera to drop the two stops by playing with aperture (so it'd have to shoot at f/8 instead of f/4) or you could use aperture priority and that would force the camera to drop two stops by playing with shutter speed (so it would shoot at 1/500th.)
Your camera probably does not have exposure compensation in "manual" mode (mine does not) -- as this wouldn't make any sense because the camera can't actually adjust the exposure in manual mode... only you can. If you want to compensate to -2 when shooting in manual, then you just use the needle in the viewfinder so that it lines up with the "-2" position on the graph instead of at the "0" or center position on the light meter graph.
Use exposure compensation when you recognize that your camera is really metering off a subject that would reflect a neutral gray value. For example... if you're shooting a dark scene or subjects dressed mostly in blacks then going to the minus side will help correct the exposure. I shoot most concert events in the minus range... usually between -1 and -2. You'd do the opposite in strong "whites". You might shoot an outdoor winter snow scene in the +1 or +2 range.
If you _really_ want to know the correct exposure, use an "incident" light meter (a hand-held meter) and not the reflected meter built into the camera. An incident light meter is basically always right.