That's wrong and not how it works at all for Madara. There are 2 factors that decide who gets the barrier in Madara's case.

1) Highest priority for barrier gets the Madara who has slowest position in your team ( 1 / 2 / 3 / 4) and your initiative completly doesn't matter in this case. If you are a whale with pos4 Madara vs noob with pos1 Madara even tho you have 100times higher initiative you will get the barrier.

^ EDIT. Actually now that I think about it have to check if skipping positions cuz of initiative also changes the order for madara barrier calculations, I don't think so but have to test it later. In general tho within 10k ini range it works like that.

2) 2nd factor yes it is initiative but only if both Madara's are in same position aka pos1 vs pos1 madara, then weaker one gets barrier.

Fun fact that most people have no clue about as well. Use ninjas like Lightning main as pos4 when Madara is support this way his barrier doesn't remove buffs like root of the warrior.