I can't speak to the causes of hypotension, but you are indeed correct, caffeine is a stimulant. As a stimulant, there is a well documented acute period of hypertension that lasts for up to 4 hours. Interestingly, there is no causal link established between caffiene consumption and chronic hypertension leading to cardiovascular disease (see here and here).
Having said that, caffeine is also a diuretic, which could cause someone who is already fairly dehydrated to exacerbate that state. It's possible to faint from a result of severe dehydration but I think it would have to be pretty severe.
It's possible someone is prone to fainting for non-medical, purely physiological reasons, such as standing for long periods, standing up too quickly, hypoglycemia, or some other predisposition.