That's correct.

I checked many times with the way some bros suggest. Put Minato first, then Bee and Roshi but nothing happened.

I think this way is correct with anyone who has the points of ninja have to match with " BEE's RECIPE ".

Example, the first ninja you put to lineup will run with a gear and this gear will make your first ninja has the condition match with BEE's recipe.

Then you know, randomly 25% of us will correct with BEE's recipe. And finally, that's not true recipe. If you don't believe, you can mixed all the gear and try it.

It won't base on the position. It base on the points. And the problem we don't know it :(

That's not correct. I checked many times with the way some bros suggest. Put Minato first, then Bee and Roshi but nothing happened. I think this way is correct with anyone who has the points of ninja have to match with " BEE's RECIPE ". Example, the first ninja you put to lineup will run with a gear and this gear will make your first ninja has the condition match with BEE's recipe. The you know, randomly 25% will correct with BEE's recipe. And finally, that's not true recipe. If you don't believe, you can mixed all the gear and try it. It won't base on the position. It base on the points. And the problem we don't know it :(

Yes, I understand how moving ninjas to switch tiles with other ninjas could mess up their gears.
However, I said I never really move any ninja elsewhere.
I only lift one ninja up and place it down to its own tile. That way, that ninja still wears the same gear.
What me and others have stated here was: It's pointless to remove all ninjas from the lineup when you could achieve the same result by just lifting ninjas from their tile, and placing it back. That way, they wear same gears, and saves the trouble of messing their gears had we removed them from the lineup.

You know why it doesn't work? Coz you were only doing it on those 3 ninjas.
Just do this step-by-step:
Arrange your ninjas to your ideal positions.
Now do this in order,
1. Lift either Roshi or Minato (whoever is your 1st move ninja), then place it back to its tile.
2. Lift Bee off its tile, place it back down.
3. Lift the 3rd ninja, place it back down.
4. Lift your main ninja, place it back down.

DO NOT remove them from the lineup. It will mess their gears up. Just do the ones I mentioned, lift a ninja up, then place it down back to its own tile.
I just tested it on Kurenai, now she always shields my Roshi first.

CAUTION: When you switch tabs, the order will be reset. So when you go back to your main lineup, redo those steps again. Switching their gears also reset the process.
Changing chakra runes will also reset it. Basically anything that alters their stats will mess the order up. Just keep doing it over again if so.

Hope this helps.

Edit: If it still doesn't work, then the problem here is miscommunication. I certainly tested it and it worked in all the times I tried. Please re-read the steps carefully.

Well tbh you probably just doing it wrong because im 100% sure thats how it works i do it all the time for space time because im always changing mains and teams. Maybe i didnt explain it well. But you c*so do it as smoe people said, you have your ninjas in the grid and move them to the side and then back at the original place, and start with the ninja you want the yo on, in this case your minato. I can record it if you want a visual example.

If the prompt move order changes, the gear equipment stays the same but the inner gates runes no.

You're talking about prompt orders relative to positions/move order, as in 1st, 2nd and so on.
Yes, runes will change if you switch the order of who goes 1st and such.
I wasn't talking about that either, and it's not even a matter of prompt order (the steps I mentioned), just something to change the target of a support mystery
to whoever you want it cast to. So, when I said "order", it meant the order in which we place ninjas into the lineup, not their actual move order.

On the other side of things, you c*ways just move the ninjas into the formation you want, then unequip all gear and then give whomever you want Bee to use Yo on with gear that gives the least amount of life. You also have to account for Moods as well.

Bee doesnt give Yo to the ninja with least hp, he gives to the first ninja to be placed in the line up