Yep, your understanding of right circuit is, er, right.
Still, if you're talking with respect to the takeoff direction, the other way of stating it is also correct, in that the aircraft turns right after takeoff and remains in that right-hand 'quadrant' with respect to the runway centreline.
Both runway and aircraft are on each others' right, so to speak. It'd be interesting to hear exactly what they didn't seem to like about what you did.