This. When a unit is involved in combat it looks for the best (most promoted) command whose command range it is within and which still has at least one command point. If it finds one then those promotions apply to the combat and the GC gets it's command points reduced by one for that turn. The combats that take place first use the GC points up in the order they happen (whether attack or defense)
Are command points and movement related in any way? In other words, does the GC need to wait 1 turn to "recharge" his command points after moving?