You need to manually set characters to creep at the end of the turn if you want them to stay alert at the start of the enemy turn. Since creeping relies on the Stealth skill, it's sometimes not worth spending the extra action point to do it—I only tend to bother with Stealth 2+ characters. Sometimes your character might have exactly 6, 12, 18 action points left, and that extra opportunity attack might be worth more than getting in the first shot on the enemy turn. So I leave the choice to the player.