Did you watch the video posted above? If it was a tail stall, the reaction has to be opposite of a normal wing stall. If it was a tail stall, pulling power and pulling the yoke is absolutely the right thing to do.
The horizontal stabilizer is a wing that produces downward lift. If it stalls, the downward lift to the rear of the aircraft goes away, leading to a nose-over, and the tail stall is worse with higher power.
I’m still trying to figure this out. If it was a normal icing condition, and stall, there would be no reason to pull back on the stick. Shoving the throttles forward would be correct, and pushing forward on the stick.
If it was indeed a tail stall, there would be lots of reason to pull back on the stick because the pilot would have suddenly found himself pointing at the ground. If that was the case, pulling back on the stick was correct, but he over did it, to overcome the stick-shaker thing. Adrenaline? He pushed the throttles forward which would be correct for a normal wing stall, though.
A micro-timeline of what happened when would help. Did he pulled back too hard, THEN pushed the throttles forward?
None of this makes sense without more information.