Bio-luminescence by the mechanism you describe would act too slowly to keep up with the pace of human verbal communication. That rules out using the colors as an extension of language, for example in place of the tones in a tonal language like Chinese and Narrow Bantu, or in place of the genders of a highly gendered language like Latin or Sanskrit. The user wouldn't be able to change 'tone' or 'gender' fast enough to keep up with speech.
Color changes would be fast enough to express emotion in speech. Irony, Confidence, Humor, Satire, etc could all be indicated by bioluminescent changes. However, this has the drawback of not being as visible during the daylight, and harder to see from a distance. If a general is giving a speech to 5000 assembled troops, its hard enough for everyone to hear him, much less to see his steely blue confidence.
The last option is as a sign language of sorts. In West Africa and among Aboriginal Australians, there are 'home sign' systems which closely replicate the full complexity of a natural language, and which some think could have co-evolved with spoken language.
The most reasonable explanation for light based communication, then, is that your people originally used bio-luminescence as a means of communication such as chimpanzees or gorillas communicate to each other. Then, as the species evolved human language with its emotions and abstract concepts (things that are absent in animal 'languages') the bio-luminescence co-evolved as a 'home sign' language. While perhaps not expressing a full range of concepts like a real language, it could express a limited subset, especially since the 'bandwidth' of sharing thoughts would be lower than with a verbal language.
Even more interestingly, it could be that the bio-language and verbal language diverged, so some groups have different verbal languages but can 'light talk' to each other when they trade. Or you could even say that the bio-language is genetically determined, and when two people can't speak to each other, they can resort to ape-like bio-luminescent communication.