Initiative ALWAYS follow the ninja's position.

A position 1 ninja will always act before position 2, who will always act before position 3, who will always act before position 4. The only exceptions are NPC-fights like Plot instances etc.

The thing Initiative does is to make sure that YOUR position 1 goes before the enemy position 1, your position 2 goes before the enemy position 2, etc. It's basically the tie breaker, and not what sets the turn order by itself. You can test that too - put all your initiative on your position 4, and your position 1 will still outspeed it if they both start doing prompt mysteries.