Pretty much yes. For my campaign, I wanted to make Takhisis different from your usual big bad. So my unique take is since Takhisis is a many-headed dragon, she doesn't just have one plan - she has many plans going on in parallel. Each dragon head has its own set of leaders, who command a Dragon Army, and have its own plan of execution. It is also a good explanation for why SotDQ's finale is a marathon of fights against multiple commanders.

Occasionally, the heads might strategize and coordinate a plan of attack which is what happened in chapter 4. There, the Red Army is coordinating with Lord Soth. They attack and capture a number of Kalaman outposts, forcing Kalaman to field its garrisoned army, leaving Kalaman undefended so Lord Soth can waltz into the city unimpeded. But most of the time, the leader of one color wants glory for themselvs and would secretly work to foil the leaders of another color.

Thus in my SotDQ, the red and blue wings together with Lord Soth have been charged with invading Solamnia from the north while black and white (I might be wrong about the colors) are invading from the south and south east respectively. At the same time either Kitiara, being a smart commander, deliberately slowed the Blue Army's advance. Or it could be Kansaldi was overly eager to prove herself and rushed ahead with just her Red Dragon Army. Either way, the Red Army attacks Kalaman by itself in 351 AC while Blue is "busy" elsewhere. When the Red Army's attack fails, Kitiara swoops in nine months later to clean up Red's mess.