This belies a fundamental misunderstanding of Yemeni society. Arab political structure is based on tribal loyalty. Leaders of tribes pledge allegiance to other tribes or coalitions of tribes. They're not part of the same command structure because such a thing does not exist. Usually instead of being defeated tribal loyalties change with the political winds and tribe leaders neogtioate with other leaders. Twitter is also ubiquitous in Arabia and the natural place for political announcements.
While that's helpful and insightful, it's not hugely the issue.
The military units are not very well organized, they don't have clear and stringent command, control and communications.
They understood a regional commander to be fleeing, units fell back.
This is kind of stuff is absolutely as old as time, and it's #1 rule in conflict aka deception.
The parallel would be reproducing a General's order to withdraw - meaning the command would have legitimacy among troops and junior officers, believing their own commanders were just out of the loop.
And yes - their command structure will be de facto organized along social lines, but it's more descriptive.
Not the military stuff but Arab tribal society, read "The First Muslim" by Lesley Hazleton, about Arab society around the year 600. It's an absolute eye-opener.
AoW is one of the most important historical treatises, it's not just 'something that was written in history', maybe the oldest true 'textbooks' of objective knowledge, and also realpolitik. Also there's hints of metaphysics in there, in a way. It absolutely stands up today.
The very first work of the Western Cannon: Trojan Horse.
Information / espionage and deception has made most of history; Hannibal, Caesar, Alexander etc.
A fun exercise would be to look at battles of history from the lens of information warfare and deception, and contemplate the outcome without it.