And here he is agreeing with the Tranquil Solution.
Hey, that's my Hawke

No, he agrees that the Rite of Tranquility is useful, but not with what Alrik wanted to do (tranquilize all mages in the world, regardless of their ability to resist demons). Cullen supports the original templar rules, that the mage should be:
1) put through the Harrowing, to prove they can resist demonic possession.
2) put through the Rite of Tranquility, if they don't want to go through the Harrowing, or show dangerous inclinations, like in Jowan's case.
3) killed, when nothing else can be done, and the mage becomes a murderer, blood mage, or an abomination.
Also, I disagree that all mages who survived the annulment would be made tranquil, because there is an option in Origins to put the survived mages into prison (I suspect Aeonar, "the trial by fire"), and after the Blight, when it's over, they return as mages, not as tranquil.
What is important to understand about Cullen is that he's not some kind of crazy fanatic, he doesn't support anything extreme, like Alrik. Templars like Cullen actually believe that Tranquility is better than death, because it means the mage stays alive, and becomes immune (well, that's what they think anyway) to demonic possession. So that's why normal templars do it, and some mages actually agree with them, because not all mages are strong enough to fight off the demon, and they know it, and the prospect of becoming an abomination scares them, and some prefer to live rather than to be driven mad by demons and killed by the templars, so they actually ask to be made tranquil.
Alrik, well, he just likes to torture mages, because he's an evil bastard, and that's why he does his Tranquility business. He does it illegally, because even Meredith told him it was not ok.
I'll repeat again, Cullen in this video agrees that the Rite of Tranquility is useful. But not with Alrik's plan.