There should be a PDF version of the manual in the download.
But anyway, as to your question, the way the software behaves is like this. When you select a ship and right-click a destination, the ship moves as far as it can towards that destination. If it can't reach it in the current turn, then it goes into Auto-Pilot mode, but at that point, since it moved in that turn, it will have zero movement points left. Since it is in Auto-Pilot mode, using the TAB key will never shift focus to that ship.
Now we hit the turn button. The ship does not move, and still says "Auto-Pilot". TAB will still ignore it. If you manually select it, you will see that it has MP left. This is all the correct behavior. If you hit the Turn button again, the ship will proceed on Auto-pilot towards it's planned destination.
To summarize, Auto-pilot moves happen after you finish your manual moves and hit the Turn button. BUT! during the first turn when a ship enters Auto-pilot mode, it does NOT move, because you already moved it manually that turn and it has 0 MP left.