You are correct about this!
A right t/r stick input should produce a NOSE right/tail left movement. Your description is definitely backwards from the norm. Should require a simple reversing of the t/r (rudder) channel at the TX. And while your "fixing" things, make sure the gyro is in phase also ... ie in rate mode, a heli nose left produces a nose right correction at the tail rotor.

As far as REVO is concerned, if your going to be spending your next dozen flights practicing hovering, then REVO is not required ... as long as your heli and TX trim are good for hovering. It's because you are going to be spending most of your torque generate fairly constant ... REVO adjusts for "theoretical" changes in torque. If/when you decide to use REVO, input small increments at first.

Good Luck,
d.tipton