The main methodology behind finding answers on the site isn't to search directly for the answer, but to search for the question that elicits that answer. Tags are only placed on questions for this reason - a tag is meant to identify what the question is about. The main reason a question may get an answer that introduces a new technology or concept is because the question author may not have known of its existence, its name, or that it was effective for the desired purposes. As such, users who would have the same question or are in the same boat would not look for that term, because they don't know what the solution is. That's why they're searching in the first place.
If the question truly is about the technology or concept that is mentioned in the answers, and the author just didn't know the term (and this not-knowing part is not a core part of the original question, to boot), then it would make sense not just to update the tags, but the question as a whole. This makes the question then helpful to those who do know the matter, as it is a part of the question.
"Is it part of the question or the solution?" This is what you should ask yourself if an answer introduces an element that you think could add a new tag. If the question is actually about that element, just not explicitly stated, then you could add it. But if the question is merely solved by that new element, that doesn't make it a question about said element.
The findability of the answer is dependent on the question it is linked. If an answer of pragmatics is something that should be found because it is a solution related to pragmatics, then the question should reflect this. If the answer merely uses pragmatics to address a question that is not itself about pragmatics, then it and the question it is attached to should not be categorically linked to all the questions that are indeed about pragmatics.