Hello, what lineups did you both have, and what battle mode were you in?

Same thing happened to me.
round 2: My position 1 gets removed from the field by Obito. Thats fine.

round 3: I get my pos 1 back, queue mystery. 2 Opponents' pos1's both go before my mystery. I don't remember if standard attack priority was affected or not, but mystery definitely gets bugged.
Happened in cross server ninja war btw.

GNW, also being strongest on the server c*most every time solo field but with chance that opponent had strong field there wanted to some support so their teams were 6p Naruto, Taka Karin, Aka-Crea Kakuzu and earth main with 6p Naruto, Aka-Crea Kakuzu, Edo Minato with barrier and earth main. 1st wave was strong so they lost both mains and support also lost Kakuzu and Minato. 2nd was triple def/res Kushina, Obito, seal Tsunade and water main. Both Narutos were sended away round 2 and as they came back round 3 pretty much always though that there is random delay to use myst but yesterday i followed it and on round 4 fastest Naruto used myst but had to wait that other mysts were used before theirs and then they had to wait that every other ninjas normal attacks were used before both Narutos were able to use theirs.

Thank you for reporting this, do either of you happen to have had or used a summon during that time?

If summons were used it happen before i got to the fight because i were on different field.

Thank you guys for reporting this, I have passed it along and hopefully it gets fixed soon! If there are any other details you can think of, please let us know.

https://www.youtube.com/watch?v=z43dJD1BMoI

2:13 Obito's mystery.

4:09 Start of round 3. Both Narutos have are slower than the opponent. Bottom Naruto even ends up getting Obito'd again who is position 2, even tho other Naruto queued up his mystery. Bug.

4:30 Both Narutos *ed in again.

5:25 Narutos are back. They are still slower than other position mystery skills.

6:36 You can see position 4 Kakuzu do his standard and only then will Naruto use his standard despite being position 1. Bug.
Conclusion: The target of Obito loses all ini. I don't have him to test a regular fight.

Thank you for providing a video as well!