So, yeah. Fiona had absolutely nothing to do with Teagan's eviction; the Venatori moved into Redcliffe beforehand and made the offer while already ensconced in the castle. Which the rebels would most certainly not be able to use for protection if they hadn't accepted it.
Except that the conversation seems to me to imply that there were already mages inside the castle. And it was my understanding that the deal that allowed the mages into Redcliffe at all was with Anora/Alistair/both, not Alexius. Not to mention that the easiest way to reconcile how easily the Tevinters took Redcliffe with how hard it is supposed to be to get in unless you've been allowed to is if the Tevinters took advantage of the pre-existing deal with the mage rebellion by pretending to be part of it like they did in order to trick Fiona into taking their bargain. (This would not be quite as effective if the rebel mages were not allowed into the castle.)
Edit: As for your basic conclusion that Fiona didn't deliberately screw Teagan over, I think you're right. Her understanding of the plan, as I understand it, is that they were all going to flee to Tevinter in short order. That not only doesn't require taking over Redcliffe castle but is something from which doing so is a dangerous distraction. Which leads me to think that that was another of the plans Alexius had that she wasn't in on. I've several times communicated a belief that she's stupid and shortsighted, but I don't think she's malicious.
No one in the game ever says that Fiona or the Mages had the option or suggested the idea of using Redcliff Castle to defend themselves so, imo, it shouldn't be used as an argument.
Considering that we have seen no evidence so far that Teagan is a heartless *******, I would be more inclined to think those who don't think he'd let the mages into his castle should have to provide evidence. (Not to mention that I think the first sentence of my response to Xilizhra provides weak evidence that he did allow them in.)