How to correctly adjust 3 speed shifter
I actually use that hub quite a bit, and was just looking into that setting for one of my customers earlier.  The "set" gear is 2.  set the shifter in 2, then yes, you want the connection from the chain to pin to be just protruding from the axle.  Once you set it like that once, lift the back wheel off the ground and pedal it one revolution forward and pedal it backwards to engage the brake once just to be sure it's engaged in the gear, and check it again.  If it has "settled into gear" and the position of that pin has changed, set it again.

Once you get it so in gear 2 the pin has stayed at that point, you should be good.  Check that all gears are working, and that it isn't slipping like you said in your original post.  Riding it for long periods of time with it slipping out of gear will wear out the internals very quickly.