The L508 is capable of metering both reflective light using its spot meter, as well as incident light, which is done using the white dome.
Although reflective metering is more common (think of light meters built in cameras), they suffer from not being colourblind. A reflective light meter assumes to be ‘looking’ at a middle grey scene. If that scene is instead white, for example, the meter thinks that the middle grey is assumes it is seeing is just very brightly lit, and thus tunes down the exposure. This is the exact reason why, with reflective meters, you want to overexpose by a stop or two when shooting snow or other highly reflective surfaces.
The same problem occurs with colour. Yellow, for example, is a highly reflective and will easily fool a spot meter. The same is true for colours that are not very reflective.
With this in mind, you should be able to see that incident metering is the better option here. Incident meters don’t measure the light that is reflected off of the subject, but they rather measure the light that is falling onto the subject, hereby eliminating the effect colour has on your meter reading.
Since I was not there when you took this photo, I cannot tell you why the face is blown out. I can however suggest a way of metering for this scene. To meter for the highlights, one should face the dome of the light meter directly towards the light source. This needs to be done while holding the meter against or next to the person’s face, as you then measure exactly how much light falls onto the face. As you may know, light intensity decreases as it moves farther from the source. Depending on how you want to expose the scene, you may want to take one or more readings. If you shoot with just the aforementioned reading, you will expose only for the highlights and you will therefore underexpose the midtones and especially the shadows. Personally, I usually take a reading of the shadows and the highlights and take a midpoint depending on my scene and how I want to expose for it. In this case, since the person/face is mostly uniformly lit, I would linger to the side of the highlight reading. Remember however that negative film is more accepting of over- than underexposure. When in doubt, shoot for the shadows rather than the highlights.