There is one thing though, by increasing the throtthe, irrespective of pitch, you will automatically reduce the pitch from the increase in speed (unless you're pointing the nose very high), though the trimming will push you back again if trimmed to a low speed, so even the power first will present some result.
Very muddled language creeping in here, back to basics. Thrust and drag = pitch up, Lift and weight = pitch down. The lift weight couple dominates the thrust/ drag couple. The Horizontal stabiliser provides a down force providing a pitch up moment. The Trim tab is used to vary the down force of the horizontal stabiliser. Increase the thrust and the aircraft pitches up (thrust can also be gained from the speed by diving which will cause a pitch up also). So, increase the thrust and the nose pitches up aided by the increase in drag, then lift/weight opposes the pitch up but not completely. Any increase in speed will be a pitch up moment aided by drag. A initial large increase in pitch may be observed if thrust is added rapidly. As the forces stabilise the pitch up will settle downwards but not to the original attitude.
So if power is used to fly out of the stall then any pitch up will deepen the stall and therefore must be opposed by pitch down elevator. If you do not have any elevator pitch down force remaining then it will not be possible to stop an increase in the angle of attack. Thus the advice to reduce power (thrust) is to reduce the pitch up forces "if necessary".