That is rubbish.

1. Your initiative on move 1 competes with the opponent on their move 1 too (Mystery and Normal attacks)
2. A move 1 will always move first followed by move 2 (Its follows in an order)
3. The only time a move 1 loses to a move 4 of opponent team is he's casting a non-prompt mystery.
4. A prompt mystery overwrites all move position, BUT still competes against the opponents initiative if his ninja is also casting mystery. (Move 1 Mystery VS Opponent Move 1 Mystery)
5. For ninja that casts barrier as passive (Darui, Danzo etc), the barrier casting depends on the ENTIRE teams total initiative combined. So if your total initative wins your opponents one, your barrier will override his.
This post was last edited by Kynareth89 at 2017-1-23 06:30

"even you put your ninja on 1st position doesnt mean you can outspeed your enemy with higher initiative than yours"

This phrase is misleading to the OP as you can tell he doesn't understand about positions and move #1. :o
So when you say that, it's like trying to tell him it doesn't matter your move number, its the entire initative the team has.