From what I understand, Orsino knew Quentin existed and had been exchanging letters with him, knew about his research, but there's nothing to say if he knew how Quentin was using this research and certainly no reason to believe that he knew before the fact that Leandra would be targetted (and at that point, he has no idea who Hawke is anyway). He might have. He might not. Given how easily Meredith leaps to using the acts of a mage completely unconnected to the Kirkwall circle as a reason to kill the entire Circle, the ugly thing is that he may well have been right that if he'd said anything she'd have used it against them. Who knows?
Even if Orsino was an active participant though, I can't understand why this would be a reason to side with the Templars. First, you don't know this until you reach him, so it's metagaming knowledge from a prior playthrough. Second, the Right of Annulment is very very very clear. Yes, you can end up sparing some mages, but there's nothing that guarantees that when you make the choice, and the only way any mages have a possibility of being spared who don't run into Hawke are if the other Templars are deliberately disobeying orders. The Right of Annulment exists specifically to wipe out every member of a Circle. The end. You don't see them, but there are children in the Kirkwall Circle, just like there were in the Ferelden one (and if you use the Right of Annulment there, that includes them too.) Look at how young many of the mages, Orsino included, are said to be when they're taken to the Circle. Remember that at this point, the Kirkwall Circle also includes every non-Apostate mage in the Free Marches. There isn't a Circle per city-state. Kirkwall has been the center of things from the start, and Starkhaven was the only other city with a Circle (and the survivors who didn't escape from that one are moved to Kirkwall). If you side with the mages at least, Varric says that many survive and flee to other Circles, so all of those mages you see in the last fight aren't even a majority. That's a lot of mages to be sentencing to death over the actions of an apostate mage who has never been a part of them, or, if you're metagaming, to spite their First Enchanter.
I can't justify a Hawke who isn't a mage-phobic **** siding with Meredith at the point you're made to choose. The guilty culprit is standing two feet away from her and has offered a full confession, the First Enchanter freaks out and condemns him too, then begs Meredith to change her mind ("Do whatever you want. Search the tower! I'll help you."), and her response is to sentence everyone to death. She doesn't even try to kill Anders. She doesn't even attempt to make sure he's going to be killed. She doesn't care who did it.