I would agree that Rand bowing to Tuon would be a factor in why the Seanchan do not abide by the Dragon's Peace, however, it seems from the visions through Padra's and Oncala's eyes that the Aiel were in fact the major causes of the world-wide war. In Padra's vision, it seems as though the Aiel are killing Seanchan who merely step foot in Arad Domon, claiming that's provocation enough for battle (and not all the Aiel agree with this, but since Padra is Rand's daughter, folks tend to go along with whatever she and her siblings say).

In Oncala's vision, we learn that the Seanchan were not interested in going to battle with Andor (or acquiring Andor's war machines). It would seem that a world war broke out because Andor was tricked by with biased Aiel intelligence into going to war with Seanchan preemptively, resulting in Cairhien, Illian, the Two Rivers, etc. coming to their aid and entering the fray.

It's far bigger than Rand bowing to Tuon. It's the Aiel's whole mindset and struggle with the Seanchan that led to their destruction and the subjugation of the rest of the continent.