Well you source is kinda … bad. In medicine a paradoxical reaction is described as a reaction which is basically unexpected. Your source is throwing things together that are not right in this way. It basically conflated research over methylphenidate, a very common ADHD medication, with all stimulants and a lot of narcotics.

Methylphenidate has no paradox reaction, because it also works in non ADHD children - just not as strong. While there are not systematic medical trials on Coffein there are a lot of weaker studies on it that show a high amount of evidence that it has a calming effect. The discussion here is if this isn’t the same in the normal population too, not if it has a calming effect.

The source you had makes claims and then does not show any evidence for these btw.