You would be partially correct (right rudder needed) in most cases, but in the case of the Nexstar, LEFT rudder is needed to counteract the excessive RIGHT THRUST at full power.

P-factor does not come into the equation for tri-geared aircraft, as they sit essentially level during take-off. Engine torque produces a ROLLING force & it also doesn't affect take-off appreciably, unless the aircraft is yanked off the ground at a low airspeed (P-factor will also have a small effect in this case, because of the high angle of attack). P-factor has a small effect on tail draggers while they accelerate with their tails down

What does give a LEFT TURNING FORCE is the spiral slipstream from the propeller, striking the rudder & fin assembly from the left side, & hence, pushing the tail to the right.

The effects of engine torque can be seen when a slow flying aircraft (with a powerfull engine) suddenly has full throttle applied -- it will try to roll to the left from the torque & turn to the left from the induced bank, plus the accelerating spiral slipstream.