Remember the uniform was copied from the French who copied it from North African adversaries in the colonial wars there in the in early 1800s. The primary weapon of the Zouave was the bayonet, not the musket or musket/rifle, which meant they fought VERY close to their foe. Their main tactic was to fight in open skirmishing order and to close the distancd rapidly to the enemy as possible. The uniform colors was most probably a means to identify them from their foes in actions that require being so close to their enemy.
The discription in battle was it looked like the Zouaves were dispersed in disorder, fighting as individuals; and without any means of defense if attacked by cavalry, however the Zouaves were taught to think as one and be intelligent enough to know when to change from dispersed disorder to concentrated order and to do so rapidly. They used the square formation better than most units. They also trained to fight from the prone position, loading and shooting while lying down (very hard to do with muzzle loaders.) Their officers duties are less than line infantry, only giving commands and guidance towards the mission's goal and let the Zouave infantry use their own instincts in combat to fight.
David