Auto barrier ninjas like Mei control the field based on overall initiative of the team.
The time of having low initiative for barrier ninjas is only when manual barrier ninjas face off, where whoever skills last overrides the current field barrier (assuming positions are the same)

Auto barier like Mei, Danzo, etc. use total initiative from 4 ninjas. Your enemy has more initiative than yours.

The total initiative matters at the end of the day.

If you are getting your auto-barrier up before the opponents auto-barrier that means your over all initiative is lower than the opponent.

I think you are just confused about how initiative works for auto-barriers and buffs.

In this specific case; higher initiative = you move later.
In practice, the "people with thousands more power than you" also probably have higher initiative, and so they trigger their barrier after you trigger yours. If you participate in GNW, you can maybe see how passive buffs and barriers are triggered. The team with lowest overall initiative will do them first and the team with highest overall initiative will apply buffs and barriers last.

For attacks and mysteries; higher initiative = you move sooner. (Which makes sense :D)

Hey i run naruto in my lineup with fire main.But naruto"s clones come up faster than my fire main"s oborono clone.can anyone tell me how to prevent that

Put Naruto last in your team, so move him and replace him last
Ninjas put last in team will cast their passiv last at start