But there isn't actually anything to suggest that. Just because both factions are lead by mages doesn't mean they are allied after all. Also, if the Inquisitor in that world state allied with the mages (which evidently she did, since she was fighting Templars on her way to Redcliffe Castle), then it makes even less sense to connect the two.
In the dwarven demo, the Inquisitor is seen fighting both Templars and mages (normal Southern Templars and mages) in the Hinterlands. Therefore, it is quite possible the first trip to the Hinterlands is when we make the selection regarding which faction to support while the scene where we see Redcliff castle being swallowed by the Fade ocurrs at a much later stage and happens if you support the mages.
As for the reasons, who knows? Maybe the mage leadership thought it could use the Inquisition while keeping contact with Tevinter allies. Our support and resources thus empowered Tevinter as well which enabled them to reach and take over Redcliff.