Nothing Changes... if you go back far enough
In premodern battles strong formations, which don't break are what everyone wants. - This is not universally true by any means. Nor is it universally true that forces which fought in such a fashion were automatically superior to those that did not. (Looking at you, Vikings-in-North-America and Crassus' Legions)
Instead what you traditionally had were raids, ambushes, and the occasional "Pitched battle" which involved warriors exchanging ranged fire (javelins, arrows, what-have-you) at roughly 2/3 the maximum distance of their chosen weapon in a loose formation. Close combat weapons were (again, usually) used only in pursuit of fleeing foes, most of whom got away. If you want the details of the whys and whyfores I suggest War Before Civilization but I think for your setting two reasons trump the others:
1: Raids and Ambushes were more effective. It's WAAAAAY safer (for the attacker) to burn down a village at night and spear people fleeing burning houses/ambush a lone hunter than fight in a pitched battle.
2: Pitched battles were un-sustainability lethal for population size.
Your battle-mages will mean these two qualities, especially the second one, are still true even after your societies start being able to have larger populations. 523
Any attempt at "ganging up" can be countered by one wizard shooting one fireball, nobody'll risk it. So battles will stay at what you might call a "large skirmish" style fight. Because of the increased lethality, ambushes and raids will still be the preferred method of warfare. After all, 15 guys, 2 of them mages, can do as much or more damage sneaking around and launching a wall-breaking fireball followed by house-destroying fireballs in the middle of the night as 1,000 infantry and accouterments can besieging a place for a year.
So what you'd actually end up having is battle-mage societies adopting "primitive" style warfare as a matter of course, and only those non-magic-using "Savages" will be stupid enough to actually stand shoulder-to-shoulder in a fight. Your system makes mass-battles far less likely in any event, as small groups can do massive damage to societies on their own. So instead of one large army maneuvering against an opposing large army and finally a battle/siege takes place, you'll have dozens or hundreds of small groups raiding into enemy territory trying to annihilate similar groups in ambushes or destroy settlements.
I should point out that the "primitive" style of warfare I described above is actually MORE deadly than modern war as a % of population, let alone other types of ancient warfare. By orders of magnitude. War Before Civilization did the math, and turns out you are more likely to die by warfare in any given year as, say, a Native American of almost any tribe we have a reliable record for (pre or post Europeans) than as a Russian OR German 1914-1945, or a Frenchman during the Napoleonic wars. So even though your "pitched battles" are rarer and might LOOK less deadly than two pike phalanxes crashing into each other, in reality the actual war will be wildly more devastating. 523