How to correctly adjust 3 speed shifter I have a second hand chapelli 3 speed bike.

Everything was fine until I got a flat tire on my back wheel.

I was able to figure out how to get the back wheel off (after a bit of Googling), by disconnecting the back shifter and thus allowing the wheel to come off.

After putting the tire back on, I realised I had moved the lock nut for the adjuster and couldn't remember quite where the shifter adjuster was previously set to. I put it back to where I thought it went and took it for a test ride and it was fine.

Recently, I have noticed that sometimes the gear slips a little (I think that's the right word for it) when I am riding and I change gear; I will be pedaling and it feels like it "slips" as the pedals will drop a little as if missing something and then pick back up normally.

I found a manual for my shifter online today, and the diagram has suggested the below is where I should adjust my shifter to:



I'm not a huge bike person and less so a mechanic and so had a little trouble following the instructions for "Gear Adjustment" on the manual I linked above. Based on the diagram, I got my shifter adjusted to the below:



Have I interpreted these instructions correctly?
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.