An SF340 flight crew experienced compressor stalls from the right engine shortly after takeoff. The reporter suspects this occurred because the Pilot Not Flying reduced the CTOT setting too quickly during his after takeoff cleanup duties.

Narrative

On initial climb out; at 1000 ft AGL the First Officer began his climb flow. He unintentionally dialed down the CTOT (Constant Torque On Takeoff) control a little too quickly causing the right engine to have compressor stalls. This led to an auto-coarsen of the right prop. We notified ATC and climbed to minimum vector altitude on runway heading while we ran the QRC/QRH for compressor stall. As soon as we turned off the auto-coarsen switch; the right prop came out of feather as we expected. We then evaluated the situation and decided to continue to destination as all indications were normal; and we determined the compressor stall was pilot induced. After letting ATC know our intentions; we called operational control; spoke to the flight attendant and then the passengers explaining the situation and our decision to continue. Initially the pilot monitoring began to run the checklist for engine failure because he immediately looked to the prop oil pressure to confirm the prop had auto-coarsened. Once he saw that it had; his first reaction was to run the engine failure checklist. I stopped him; explaining we still had Ng (free turbine RPM) of 95%; normal ITT and fuel flow indications as well as engine oil pressure and temps in the green. He then ran the proper checklist for compressor stall and resolved the problem.I know that I was taught in initial to be very slow when dialing down the CTOT so this doesn't occur. When discussing the event later with my First Officer; he did not think he dialed the CTOT down too quickly and informed me that he did not recall ever being cautioned about that before or in training. One suggestion would just be to make sure this is consistently addressed in every initial class or simulator session.