Caffeine also activates the release of glutamate, which, is an excitatory neurotransmitter. Part of that "stimulant" effect. Having said that, many autism variants are low in gamma-aminobutyric acid (GABA) the inhibitory neurotransmitter that breaks down glutamate within the synaptic spaces. Excessive glutamate/insufficient GABA can be an underlying cause of repetitive thoughts and actions, "stimming" for example, or difficulties transitioning from one thought or action to the next.
Obviously, some people will be more sensitive to the effects of caffeine than others, but I suspect that more people with an underlying autism condition may be particularly sensitive in terms of their thought and behavior patterns, even if they aren't getting the increased heart rate, high blood pressure, and "jitters".
The increased dopamine may be a benefit for those same autistics with poor dopamine turnover and an underlying depression though. It's one thing to drink coffees and teas, drinks with relatively low levels of caffeine, but some caution when it comes to some of those so-called "energy drinks" with 160-300mg of caffeine.
Interestingly, the addition of L-theanine, say a 100-200mg dose, with your coffee or tea will have the effect of (1) lowering the overall peak in caffeine level, but also (2) lengthening the time of the stimulation. Instead of having a short-term "high" and then a quick drop off, you have a long-term "moderate" effect.