Starting a sentence with a phrase like When a hyper person drinks coffee brings about an awkward situation. Which pronoun do you use as the subject of your sentence? Using just he or she can be viewed as sexist, and using one sounds way too archaic.
People are moving towards accepting they as a singular pronoun in these situations. Grammarians are finally beginning to realize what we've all known since the third grade: using he or she sounds crappy. But using they as singular is still a bold move, so only use it in more informal settings or when you're prepared to defend yourself.
If none of these options work for you, rewrite the sentence to avoid the problem entirely. For example, When people who are hyper drink coffee, they tend to bounce off walls.