Chances are that, had he not been enthralled by Corypheus, Alexius (the guy used to be Dorian's role model after all) would have remained true to his word.
Alexius wasn't a thrall of Corypheus. He was a free willed agent, not a mind-controlled slave- and his reasons for coming to Redcliffe were as that agent.
He never would have had presence, or opportunity, to offer his word had it not been for Corypheus. Alexius's agenda was never to help Fiona and the mages escape.
Fiona throwing in her lot with one of the few honorable Magisters wasn't a stupid decision, just one based on outdated information.
No, it's still a pretty poor decision- because Fiona's failures are in the lead-up to the decision and the foreseeable consequences, not the unforeseeable consequences of the Venatori surprise.
The only goal that Fiona's pact with Alexius might have achieved would have been 'escape to Tevinter'- but 'escape to Tevinter' was not, and never had been, the goal of the mage rebellion. And that's without the huge qualifier of 'as slaves.' If Fiona fled to Tevinter, her Mage Rebellion ends as a catastrophic failure, and hands the Templars an even greater victory that they wouldn't have otherwise been able to achieve.
The Mage Rebellion wasn't an exodus movement- it was supposed to be an emancipation uprising in which the mages of Southern Thedas would break and/or reform the Circle system. To change the status quo, and give the new mages of the future a new state and slate in life. Either through a military victory against the Templars, or a political compromise that favored them. Militarily, the mages lost- hence why the last of a international rebellion was holed up in the sanctuary of Redcliffe. But politically, all they needed was to stay in the game and avoid total defeat.
Which is what the Redcliffe sanctuary did. Alexius, honest or not, didn't save the Mages from total eradication because the mages weren't facing total eradication: there was never a Templar host that could credibly conquer Redcliffe and the Castle, nor has there ever been any credible evidence provided that the mages wouldn't have been allowed to take sanctuary with the rest of the town in case of attack. By the time of the Conclave, the mages are in a very strong position: even though their military is defeated, the Templars can't beat Ferelden, and Ferelden's protection means the Templars can't attack the mages without attacking Ferelden as well. The mages might not get everything they wanted, but they have a security patron who's invested in defending them, and reforms are far more likely than the Chantry supporting or tolerating the sack of an Andrastian settlement by the Templars.
Fleeing to Tevinter abandons that. It leaves the Templars as the only force in the field- and no one left to stand in opposition to them as they lead the reconstruction of the Circle system. The Chantry can try to make some reforms, but it'll be nothing like a dedicated interest group interested in mage rights- and that's before all the political hay to be made out of the inglorious end of the Mage Rebellion.
Defeated, abandoning the principles of the uprising (slaverey over freedom), fleeing to the hated Tevinter, and abandoning the world in a time of crisis to save their own skins. This is the consequence of if Alexius were honest and kept the spirit of his bargain- a Southern Thedas in which the next generation of mages comes under an even more Templar-dominated Circles, in which the mage movement is deligitimized and the Templars vindicated.
Don't believe me? Just think of how it'd play out going by the game.
Let's assume the smallest change possible- that Alexius's son never gets the Blight. That without the need to save him, Alexius is good, not involved with Corypheus, and wants to take the mages to Tevinter out of the goodness of his heart. Maybe he has benevolent self-interest in making a powerbase out of them- he brings them north, they serve their contract in good care, and they become supporters of him.
So Corypheus triggers the Breach. Chaos. Alexius, sensing an opportunity to save mages/help himself, uses time magic to approach Fiona, pre-empting her going to the Inquisition. For the sake of the position, let's handwave the role of the Venatori infiltrators in convincing Fiona to sell her people into slavery. Let's say that good!Alexius simply offers better terms. Fiona agrees, and because Alexius is good and not evil, there's no coup in Redcliffe and no ousting of the Arl. The mages head north across the lake, avoid the demons, and Alexius has the means to have ships waiting for them.
What happens to the Thedas that's facing the demon apocalypse?
Well, the Inquisition's goal is to close the Breach, and to do that it needs mages or Templars. All the mages just abandoned Thedas, and while the timetravel dejavu is strange, they're gone because Alexius didn't make them stick around. Templars recruited it is.
The Templars close the breach. The Order, or at least the foundation of it, is preserved- but the 'mage freedom' movement is not. The Mage Rebellion is either dead, or currently serving as servants in Tevinter, meaning that it's the neutrals and loyalists- the ones most interested in the Circle of before- to represent the mages, even as the Templars are still around.
The Divine can try to make a difference- Circle vs. College and all that- but in order to have a viable 'mage freedom' movement you're going to need, well, mages who want mage freedom. And that movement is going to need popular support.
Fiona's actions, even if they don't doom the world if Alexius is honest, forfeits the argument. The Templars, and their successor organization, are the ones legitimized by helping save the world. The Templar arguments- such as that the mages can't be trusted to police themselves- is validated. And the Mage Freedom position- the one for radical reforms and to trust the mages- all it has left is the fact that it lost the war, betrayed its ideals and Andrastian norms by selling itself into slavery for security, and abandoned Southern Thedas in it's darkest hour. That's the legacy the mages of Southern Thedas will have to deal with.
All to save themselves in a desperate deal with a foreigner who could have been a viper at their chest... when they're lives weren't endangered.
That's not good leadership for Fiona, leader of the Mage Rebellion, aspiring to change the system of Southern Thedas for her people.
Her behavior in Asunder was much more untenable: there she was clearly lusting for a fight she couldn't win. In Inquisition, her people were holed up in Redclife, while Templars were going on a rampage in the countryside (thus robbing her followers of the possibility to police themselves, since they'd be slain by Templars if they even attempted to leave Redclife to go after the mage supremacists burninating the peasants), the Fereldan monarch had granted asylum to the mages against the nobility and commoners' wishes*, and the last attempt at diplomacy at literally blown up in everyone's faces.
While the mage supremacists were between the Templars and Redcliffe- the Templars weren't in the way of that- your first part is correct. Fiona was unreasonable and not particularly rational from the start of her rebellion.
The difference between Fiona of Asunder and Fiona of DAI isn't that she's OOC. It's that the character who was prone to reckless, grand mistakes is now dealing with the consequences of reckless, grand mistakes. She's eating crow- if not exactly humbled.