Initiative doesn't matter in most cases because most of the time your enemy and you will be casting from different positions. The move order of your ninjas is what's meant by position as it's determined by where they are in relation to other ninja on your team.

When speed is called for, the game checks everyone to see if they are using a Prompt jutsu. If they are, it has all the Move 1 ninja use their jutsu first. Then the Move 2 ninja. All the way to the Move 4 ninja who are last. Initiative only matters if you and your opponent are both trying to use a jutsu during the same Move order.

The reason his Tobi is acting before you is because his Tobi is probably at Move 1 or 2 while your main is somewhere around Move 3 or 4. To act faster you have to move the ninja you want to be "fast" higher up the move order. Tanks are usually Move 1 so they act before everyone else. Move him to be the tank or put him above the tank.