General only appear in mid-battle if handicap on. Yes, I'm 100% sure about this. Just try to melee with handicap off, and after thousands of battle, no general will appear. Now try with handicap on and I'm sure you will find general mid-battle after some battles. Sadly, not much people realize this fact, or at least, that's what I think until now.
I come to this conclusion from all of my farming until now, I've never seen general appear mid-battle if handicap off until now, and if handicap on, I met them every 5 battles or so (except if I'm really really unlucky).
Oh, and 1 more, I think this rule apply only for musou battle, I'm not sure if novice and veteran battle has the same rule or not.