Orienting the head differently measures different things with the incident meter. It can be used to determine exposure settings, or can be used to determine contrast ratio.
Pointing an incident meter at the camera gives you a reading of the light that is "falling on the scene the camera can see" and that reading will place subject exposure to look "normal" under that light. This normally ensures a camera setting that provides good detail on both sides of the face.
Pointing the meter at the main light source will make the dark side of the face look very dark. Pointing the meter away from the main light source will make the Darkside look brighter. You can use any angle in the middle to determine how bright or how dark you want the subject to look.
That is all about placement, contrast is a different matter.
To measure contrast I normally retract the dome.
Pointing the meter at the main light source will then give you a reading of how bright the main source light is. Not the camera setting.
Pointing the meter at the secondary light source, whether that's a reflector or a dark area that's "lighting" the dark side of the face, gives you reading on how bright it is on that side. Again this is not a camera setting. (This can also measure the difference between various studio lights.)
The difference between these readings is the ratio of contrast. So if the light on the bright side is three stops brighter than the light on the dark side, the ratio is 3:1.
With careful placement you can't get a high contrast (3:1) shot with details on both sides of the face.
Those that recommend simply taking a meter reading pointed at the light source as the camera setting are making assumptions about what you want from your photo. Typically that type of reading will provide very little if any detail on the dark side of the face.
Is that what you want?
If not then you have to find a compromise that will get you what you want.
That's not as hard as it may sound. If the lighting ratio is right (whether that's 2:1 or 3:1 or 1:1) then a normal (pointed at the camera incident reading) will get you in the ballpark for camera settings. The fine tuning is done when printing if you are using negative film. If you are using transparency film you will need to be more accurate on camera setting and that will come with experience and you will learn to judge the angle of the incident meter head to get what you want.