I would disagree if I thought Bioware had done it on purpose. As it is...
BioWare is intentionally vague in a lot of what it writes because it wants to leave things up to interpretation, I believe. It seems that this particular situation is not one of those times, however, because the lack of a specific timeline of events does not make sense. I can't see a reason why we know exactly what when down with the Templars (Envy, top-down infiltration, etc), but all we get is some sketchy timeframe for the Mages (at some point, Alexius shows up and takes over the castle...period). There's no need to define when the Templars were infiltrated because we know the surrounding events exactly, and there's no time magic involved. In a scenario in which there's time magic (the Mages), we know surprsingly little about time. It's something that should have been explained or worked out for everyone's sanity, haha. The Mages scenario is so much more complex because of the time magic, but also because they're hold up in Redcliffe after being granted sanctuary by the Ferelden Monarch, whereas the Templars are an abandoned fort (I think it was there's previously?), which is a much simpler predicament. We know the Templar leaders willingly accepted Red Lyrium, we know that the Envy demon took over Lucius's place, we know the corruption came from within the organization's leaders accepting Corypheus (Samson). It would be nice to know when Envy took over, but we have enough information to accurately place blame. All we know about the Mages is that Venatori infiltrated them, which somehow led Alexius to get Fiona to agree to the alliance (whispers about a Templar attack? Secretly pushing for Tevinter alliance? These are suggested, but very unclear to be sure), which somehow led to Alexius kicking out Arl Teagan from the castle (completely unexplained) after arriving via time magic, which occurred at some point in time (No idea when they took over, only that they arrived a couple days after the explosion). My point is, although BioWare strategically uses leaving information out regularly, this is either a) overdoing it if it's intentional, or
some sort of oversight in the writing process/cut for resources like time or budgey. I refuse to believe their writing is just so sloppy to leave questions like this and they did not realize it, the rest of the story (and all their other games) are too good for that.