Torune is not delayed, read about "[promt]" effect which is written near each mystery. If that player has no "[promt]", then it means his mystery will only work when his turn comes, or if you activated after he has made his turn, then he will use it next round when his turn comes, like Gaara etc.

About topic in general:
I really dislike these kinds of investigations/reports, gives the impression that developers/moderators, etc. people controlling the game no matter in what way, do not play their own game since for them the bug would be a lot easier to under if they played themselves time to time and understand what is wrong where.

- Is it affecting only specific ninjas? -No, every ninja is affected whose mystery is [promt]

- Is it affecting all special skills? -[Promt] mysteries are affected.

- When are you experiencing such problems? -Every time I play pvp.

- Is it happening during specific in-game timed event or is it random? -Explain "specific in-game timed event". If it's event related, then no (obviously). If it's fight/battle/duel related, then yes. Is it Random? unsure, sometimes works, sometimes doesn't, then probably random.