When talking about war between Dales and Orlais and Exalted march, there are a couple aspects we should consider. I thought about it for a bit and came to two conclusions: first of all, "Exalted March of the Dales" came to be the name for the entirety of the war, even the part before the Exalted March was declared - and likely Chantry was in fact involved in the war right from the beginning, again - even before anyone called it an Exalted March (this makes even more sense when we remember that it was the first time anybody used the name for anything other than Andraste's campaign and Orlais already fought for faith while not calling it Exalted Marches.
This blurs the line between "normal war" and Exalted March, which is a good thing, since people (educated people) seem to generally accept Red Crossing as the event that led to Exalted March - preposterous claim UNLESS the whole war is called Exalted March even before Divine named it as such.
The second aspect would be of the "who shot first" variety. There are, generally, two options: after Red Crossing (let's assume it as the most severe in a series of border incidents) the Elves marched with their army and took Montsimmard or Orlesians attacked the Dales in force and were immediately pushed back into their own territory. The first would make a bit more sense from military standpoint (underestimating enemy you want to attack is one thing, but underestimating him to extent leading to such a crushing defeat right at the beginning of war?) but the latter would be much more consistent with apparent elven politics. Basically, neither scenario sits well with me, but after thinking a bit, I'm now almost sure that it was indeed Orlais+Chantry that actually made it into a full-fledged war. Otherwise why would anyone consider Red Crossing as a cause/trigger for the war? The war didn't start as follow-up to Red Crossing, but rather as reaction for it. Take this codex (it's not the only one that suggests this chain of events):
http://dragonage.wik...ch_of_the_Dales
It supposedly circulates among the educated elites, they - no doubt - know of the extent of elven victories. Yet still Chantry is credited with attacking in response to Red Crossing and the events in the village are even questioned. The author is almost certainly wrong, we have no account of false-flag operation (I put "almost" for possibility that humans wiped out the rest of the village to incriminate elves as monsters who massacred a village rather than killed a bunch of armed villagers near said village). But it doesn't matter for us at the moment - what's important is the fact that anyone could consider false-flag operation supposed to give Orlais/Chantry an excuse for invasion. Now, were it the elves who invaded afterwards, it would make absolutely no sense.
So, I think we should consider canon the chain of event:
1. Border incidents that lead to
2. Red Crossing that's used as excuse for
3. Orlais (with Chantry already actively involved) making a move on the Dales, but underestimating them to such an extent that
4. Dales crush the invading forces and go on counteroffensive, capturing Montsimmard after which
5. Chantry (already fighting in the war from the very beginning!) declares the already-in-progress war to be an Exalted March against the Dales, the name that will later stick as the name of the whole conflict.
At least that's the only idea I have for reconciling codex entries about Red Crossing being the cause for Exalted March with what we know about the first stage of the war 
Admittedly, it may still seem somewhat far-fetched, but we have little choice if we want it all to make modicum of sense - after all we can't even just write it off as retcon since both confirmations of Dalish offensive and the abovementioned codex entry come from DA:I and are completely new lore rather than something recycled from previous installments.