Varian doesn't scold her about not having the authority. He scolds her because he was securing relationships with the Blood Elves, which Jaina undoubtedly soiled with her actions. In fact, he TRIES to scold her about it, and she shuts him down.
(Commented on wowhead with the quote:
https://www.wowhead.com/quest=32423/...-done#comments )
But:
1) It's a direct contradiction of your own events as you say they occurred. Which did? Did she attack them in the streets, or did she only attack those who were hostile to her? These are two very different versions of events, and neither tells us which is real. If you can't prove her attacking the Sindorei in the streets is any more Horde bias than the 'alliance bias' in them being teleported, then you're only talking headcanon just as much as I am.
2) You still haven't proven she "punished" anyone who wasn't breaking the law. Those who complied were either let go or freed offscreen at some point, since they're back in Legion.
It's a reddit post literally describing what happens in game, which is clearly supported by the wowpedia article you yourself linked. It's not meant to be read as anything other than a statement of fact that can also be read within your shitty wowpedia article. What they feel about the purge is irrelevant to the information within the post.
But here's the quote from wowpedia since that seems to be your bible:
https://wow.gamepedia.com/Purge_of_Dalaran
The only time "kill" or "eliminate" is mentioned is against hostile/lawbreaking targets (uprising, magister breaking the law, refusing to side with Silver Convenant) when the dragonhawks are concerned, together with "subdue" and was meant moreso to prevent them from leaving the city. Which is common practice for lawbreakers, deny them the ability to travel.