I thought of precise, but not entirely sure even after checking a dictionary. Would you think it is the best choice?
Precise is usable in the sense you suggest, but it may be used more often to refer to ways of speaking rather than to accuracy of vocabulary. For example, I think that the following sentence from the Agent(The_Matrix) wikipedia article refers more to how Agent Gray talks and how he limits what he says, moreso than to vocabulary:
Like all Agents he is normally dispassionate and aloof, with a precise manner of speaking, but ...
As alternatives to precise for speaking of "someone who uses the right vocabulary consistently", consider fluent, "Able to speak a language accurately, rapidly, and confidently". To some extent, fluent emphasizes ease of speech more than accuracy, but a speaker or writer who often uses incorrect vocabulary will not be thought fluent.
Some fluent synonyms include articulate, eloquent, facile, flowing, fluid, glib, liquid, mellifluous, silver, silver-tongued, smooth, smooth-spoken, voluble; of these, a few like articulate (speaking in a clear or effective manner), eloquent (effective in expressing meaning by speech) are directly relevant. Most of the rest emphasize delivery (how one looks and sounds) more than content (what one says), I think. Well-spoken, however, usually refers to content as much as delivery.
Literate, "Knowledgeable in literature, writing; literary; well-read" is another word to consider.
From the dictionary, I suggest expressive.
Precise, exact (but not "exacting"), correct.