It is simple to theorize, and easy to prove; in uneven lighting (i.e. not 1:1), if you point the dome at the camera, you overexpose. Plain and simple. This is because the dome is not measuring the actual light falling on the brightest side of the subject (which is what you should expose for to get a "proper" exposure), but is measuring less light, due to "dilution" with the reading from from the dark side.
To get the textbook "correct" exposure, you should point the dome at the light that is illuminating the part of the subject that you want to be most properly exposed. This light could be a studio lamp; it could be the sun. It could be surrounding plant life – a field of grass, for instance; it could be a bounce card or a wall. All that matters is that you point the meter toward the thing – or toward the "general area," in many natural lighting situations, which tend to be much larger than studio sources – that is providing the most light to the part of the subject that you want to properly expose. The shape of the dome accounts for all other light that is illuminating that part of the subject, e.g. spillover/flare from other light sources, light skimming in from the sides, etc. This is the beauty of the dome, not that it is shaped like a human head for the purposes of averaging two lights in uneven ratio.
If it is hard to visualize why this happens in theory, try it out on some transparency film or instant prints to see it in practice. Set up a 1:1 ratio, a 2:1, 4:1 ratio, and so on and so forth. For each different lighting ratio that you set up, make two exposures: 1) dome facing the main light, and 2) dome facing toward the camera.
In totally even lighting, the 1:1 shot, you'll see that it doesn't matter where you point the dome; you're going to get the same reading.
In the 2:1 shots, you will see that the shot metered for the brighter light has a correct exposure on the bright side of the subject, and the darker side is where it is expected to be with that lighting ratio. In the shot metered down the middle, you'll see that the brighter side looks about 1/2 stop too bright, and the darker side appears about 1/2 stop lighter than you would expect it to appear in that lighting ratio.
In the 4:1 shots, you will see that the shot metered for the brighter light has a correct exposure on the bright side of the subject, and the darker side is where it is expected to be with that lighting ratio. In the shot metered down the middle, you'll see that the brighter side looks about 1 stop too bright, and the darker side appears about 1 stop lighter than you would expect it to appear in that lighting ratio.
In other words, if you meter down the middle in uneven ratio lighting, you will overexpose by half the difference in stops between the two sides. This is easily overlooked with negative film, as the actual lighting ratio is not severely changed; you just have "global" overexposure of the image, which is naturally compensated for when test stripping. But do it with a Fujiroid, a transparency, or digital, and you've got a problem.
If you want the most accurate representation of the lighting ratio that exists at the subject, you should meter the strongest light that is illuminating the part of the subject for which you want to expose. If you specifically want to average the main and the fill (i.e. deliberately overexpose), which you may want to do in order to prevent futzing about when working with negative film, then you can place the head of the meter on a line between the main and fill lights. In cases in which the two lights are on a plane parallel to the film plane of the camera, then yes, would be pointing the dome at the camera.
And there is no difference in theory between outdoor and studio light. What differs are the specifics of isolation and control, and the fact that sources outside are generally far more broad. But light is light; it all behaves the same. It is either even or uneven, and you should meter accordingly in any situation. Outside there is always a main source of light (e.g. the sun on a sunny day, the grey haze on an overcast day, or the sky and surrounding objects when shooting someone in open shade); there is also a less intense light coming from other directions (e.g. reflected light from the ground, sky, and/or buildings). In the event that both of these have an equal effect on the subject, you can point the dome at the camera and get a textbook exposure.
And, of course, you point the dome at the camera if the light is coming from the direction of the camera. That goes without saying.