Countersteering would tend to put the right wheel back down. It also would send the trike in a straight ahead direction, and you would miss the curve!
Your bike, with the voyager attachment steers exactly like a trike, or even a 4 wheel atv. Any attempt to countersteer could cause a disaster. The inside wheel lift is of no concern to the operator; it is only a problem to riders behind that even notice it happening.
Due to the lean factor, your car has less downward pressure on the inside tire, and increased downward pressure on the outside tire.
My favorite analogy, is to think of a trike's (3 or 4 wheel) handling more like a sports car than a bike. You slow down entering the turn, then roll on the throttle as you proceed through the turn, and you will feel the rearend push you around and through the curve.