On road, I never like to think of initiating a turn by turning your front wheel either direction, that's a quick way to end up on the ground. I think of it more as counter-balancing than counter-steering. Weight on outside foot, inside arm straight. So both 1 and 2 are I guess correct, but I don't like to think of it as turning my bars if I'm on my road bike. All I ever really think about is my outside foot - if it's properly weighted I can point the bike wherever I want through the turn.

If you really want to feel counter-steering, get on your MTB on a moderately fast downhill with sweeping turns. With the slower handling you can really practice and feel counter-steering as the back wheel drifts a little.