The Initiative parameter defines which of the fighting troops striked first. Troops that have a higher initiative always attack first. However, this bonus only works once per round. A round is considered completed when all of the attacking troops had a chance to strike the defending troops and vice versa.
If the initiative of confronting troops is equal, then the first hit is determined randomly. You or your enemy have a 50% chance of striking first.
Note that Engineer Corps only have bonus initiative when fighting troops with a “Fortification” trait, while Fortifications have a higher base initiative against all types of troops.