Is there a word which actually means the common incorrect usage of the word "reactionary?"

At WinEveryGame there is a narrowed definition of impetuous that fits, but I'll add the broader dictionary definitions they give:

Impetuous is an adjective which describes a person or a thing, usually an action or idea, as arriving at an outcome impulsively or without much critical thought.

........

impetuous [adjective]

• Acting or deciding upon something with little to no forethought

• Aggressive or instantaneous in nature

..........................................

Colloquially, they

shoot from the hip.

From Lexico [US Dictionary]:

shoot from the hip [phrase] [informal]

react suddenly or without careful consideration of one's words or actions.

• In the book he shoots from the hip and rides roughshod over reputations, holding a modicum of his once monumental power and relishing it.
• To some he is difficult to take seriously, and he may come across as the sort who shoots from the hip with little thought for the consequences.
• I know that she shoots from the hip and is liable to provoke righteous indignation.
• He doesn't shoot from the hip but takes a more considered approach and would rather explain to people why he holds the views he holds than intimidate them to his point of view.

I haven't encountered this kind of improper use of reactionary before, and while there's no very good single-word replacement that's also an adjective, there's a phrase that means exactly that: to jump to conclusions

People who think that this athlete is over the hill based on a single poor performance are just jumping to conclusions.