I think there is little doubt that "reaction" refers to the "equal and opposite reaction" of Newton's third law.
First consider "reaction control system". In principle, that can include both thrusters and reaction wheels, but in the Kennedy Space Center website it generally refers to thrusters. And the term "reaction" from Newton's third law is very closely tied to rocketry. For instance, consider the second sentence here:
Rocket thrust is the reaction force produced by expelling particles at high velocity from a nozzle opening.
Now consider reaction wheels. Reaction wheels, like thrusters, do in fact depend on Newton's third law, so, if in fact it is true that "reaction control system" refers to reaction in that sense, it makes since that the "reaction" in "reaction wheel" does too. The fact that reaction wheels, which function based on producing an equal and opposite reaction, are distinguished from gyroscopes, which measure changes in orientation by orthogonal torques, further supports that idea.
It is hard to find a source explicitly saying that is why they are given that name. But the centrality of Newton's third law to rocketry makes it hard to imagine it could come from anywhere else.