OK. (The terminology of 'action' and 'reaction' is a bit old-fashioned.)
An odd term, but OK. Let's call the mass of interest mass A. Note that the force on mass A must be exerted by some other mass or object, which we can call mass B.
Sure, if you switch to analyzing things from the non-inertial frame of the accelerating mass there will be an inertial force due to that change of reference frames. It's not a 'real' force and it's certainly not the 'reaction force' to the force on mass A. The Newton's 3rd law reaction to the force on A is a force on B