I have Nikon camera so I can't speak for other brands.
In full Manual mode (Auto ISO = OFF) exposure compensation does not work. It has no effect on exposure. That's why this mode is called Manual. You need to manually set the time, aperture and ISO value for a proper exposure. I set the aperture for the desired depth of field, I set the time I need for the shot (stationary or moving subject, ….. etc) and then I set ISO for proper exposure.
I usually use this mode when the light is more or less constant – for example, shooting an event in a gym with constant lights.
When I shoot in Manual mode with Auto ISO=ON, camera calculates proper ISO value by itself for proper exposure.
I set the aperture for the desired depth of field, I set the time I need for the shot and camera sets the ISO value. In this mode I can use exposure compensation to tell the camera to use different ISO value – I can change ISO value with exposure compensation.
I use this mode when the light is not changing a lot and I have no time to set all parameters manually.
When the light is changing a lot (for example, outside – bright sun, deep shades, …etc) I usually shoot in aperture priority with Auto ISO.
First I set the longest time the camera can use (for example 1/125 – the camera won't set longer time then 1/125). Then I set the aperture to control the depth of field.
The camera will set proper ISO by itself to get proper exposure. It will start with ISO 100 and first try to change the time. If I shoot in the sun and I set aperture to f8, the camera will set other parameters to, for example: 1/640, ISO100. If I then move to deep shade with low light and with f8, the camera will first change time. If the light is low enough, the camera will first change time from 1/640 to 1/125 limit, then the camera will use higher ISO to get proper exposure.