What you've found is correct. Using E-TTL II, flash metering happens just before normal exposure. It works by sending out a test flash to see how well the flash is able to illuminate the subject. Prior to that test flash, the camera has no way of knowing how much your flash will be able to contribute to the illumination of your scene. For all it knows, the flash may be able to properly illuminate your scene using only a fraction of full power, or it may not be able to make any change at all, even at full power. This is even more pronounced if the flash is a remote one, tucked away somewhere to the side of the subject. The camera has no way of knowing if you even aimed your remote flash towards the subject or not, prior to firing the test flash.
Since the metering of ambient light takes place before firing the test flash, it has to totally disregard your flash. Well, as you have already found, it doesn't do that, since depending on your exposure mode, it may adjust a bit to make use of the flash possible.
But in M mode, it's up to you. By selecting a combination of aperture and exposure time you select how much you want to suppress the ambient light in your picture, something which in turn will determine how large a portion of the total illumination the flash will provide. Centering the meter will provide what the camera considers to be standard exposure already without the flash. Thus adding ever so little more light will give you an overexposed image. Since this is M mode, it's up to you to decide how much you want to underexpose ambient, when providing some space for the added light from the flash.
If you use Av or Tv, the camera will reduce the exposure of the ambient by about one stop, taking a chance that the flash will be able to fill in the lacking part. It may or may not, but it can't know until flash metering has been executed.