If you light the Hilite internally, why would you be trying to meter incident light? Until you add front lighting for the subject there is no incident light to be metered. The Hilite on its own needs to be metered as a reflected light source. If you want white to look white then you need it to reflect back (or in this case emit light) at least 2 stops brighter than middle grey. You're not going to see the background clipping at only +2 stops, not unless you add a good dose of extra light from the front.
If you are going to front light the Hilite then you will be measuring incident light and +0.5 to +0.7 stops brighter incident illumination should be enough.
If you do have your subject very close to the Hilite then obviously it is going to pick up a fair amount light from the key light, and that is not only going to reflect back to the camera but also splash all over your subject, moreso if your Hilite is large relative the the subject and distances involved. You might want to dial down the Hilite itself, but it would probably be better to move your subject further away from the Hilite. That'll give you advantages through distance and reduced relative size.
In theory (only) it's transmitted light
but some of that light is also reflected light, simply because light transmitted through it also reflects off of the less than perfectly flat surface of the diffuser. Would you describe light bounced off of a reflector as transmitted? No, it's reflected, and this is similar.
And you can measure by incident light, simply by pointing the flash meter receptor at it from zero distance, the meter will, as always, measure the quantity of light incident upon it.
What I'm about to say sounds critical of the Hi-Lite, but it isn't meant to be. The Hi-Lite is a very useful tool, especially for people who are very short of space, but the principle on which it operates is flawed. Because the light is transmitted the whole of the diffuser becomes a light source, and it travels in a straight line right at the subject and right at the lens. The light that hits the lens causes flare, sometimes this is obvious and even when it isn't it reduces the overall contrast. And light that hits the back of the subject is far more likely to cause edge degradation than a paper etc background because the traditional method of lighting a normal background is from an oblique angle, and although a certain amount of light will obviously bounce onto the rear of the subject, cosine law means that far less will reach it because of the angle of reflectance.
Hi-Lite backgrounds don't benefit from the effect of cosine law, so it is even more important not to overexpose the background by anymore than necessary. You're absolutely right when you say that it helps to increase the distance from subject to background, but the fact of the matter is that people buy them because they want blown white backgrounds in small spaces - which is a bit of an oxymoron - and they often simply don't have the space to move the subject away from the background.
As with everything to do with lighting, an understanding of the nature and behaviour of light (basic physics in other words) is a massive help. But testing is a massive help too, and my advice to anyone who doesn't know whether to follow Lastolite's advice of overexposing by 2 stops or to follow my advice of overexposing by about 0.7 of a stop should simply test it for themselves.