it's the other way around, scientists believe people with adhd have lower levels of dopamine in certain areas of the brain which causes them to seek constant stimulation in order to get the same dopamine release as normal people, thus causing hyperactivity. it also explains why long periods of concentration are difficult since it provides very little stimulation. stimulants release more dopamine so this has a calming effect because they no longer have to be stimulated in order to achieve a satisfactory level of dopamine.
if you think about it, stimulant abusers build a tolerance to the drug, which decreases their baseline dopamine levels (the amount of dopamine when they're not on drugs) when compared to someone who doesn't abuse stimulants. this causes them to become addicted because their brains are telling them they're low on dopamine and need stimulation (or a stimulant) in order to get back to a normal level. there's also the psychological addiction to the feeling of being high but i'm just talking about the physical component. if you relate this to people with adhd, their brains have less dopamine, which is telling them they need stimulation, so they become hyperactive.
one thing that is under investigation is the possible treatment using dopamine antagonists. they've explored a similar concept with asthma treatment. asthma is frequently treated with stimulant type drugs (beta-2 agonists) which act on the adrenergic receptors in the brain to relax smooth muscle and relieve inflammation. the idea of using beta blockers seems counter-intuitive but the reason it works is because your brain develops a tolerance to stimulants, meaning it will lower baseline levels of whatever neurotransmitter we're talking about, so if you medicate with an antagonist to that neurotransmitter the body will adjust by raising baseline levels. what they started doing with asthma is they would give daily doses of a beta blocker for, i believe, about 9 months. during this period the symptoms would be worse than usual and would gradually get better as the body adjusted to the drug. once the drug treatment was discontinued the patients experienced improvement in their condition and many no longer needed an inhaler to treat their symptoms.
so that idea is now being investigated for adhd. the idea is similar, treating people with adhd with a dopamine antagonist will increase normal dopamine levels so once they stop the treatment the symptoms should improve. there are a few problems with this idea, mainly that it would make the symptoms of adhd worse during treatment which would make it difficult for these people to function adequately in school and/or work, but scientists are looking into it.