The reinforcements will come into battle to replace the current army's units. They do arrive in an order, if you look at the reinforcing army before the battle, the units from it will join the battle in order of left to right, top to bottom. (IE, the same way you read in english.)

So I know WHAT I'll get when they arrive. The downside is, there doesn't seem to be an easy way to arrange the order of units within a single army... only by shuffling them between armies (and using up movement doing it).