Siege question

[Snacktime]

Let's say an enemy is besieging my castle, and has breached the walls. If I move troops in from another territory, and at the same time he orders his besieging troops to storm the castle, what happens? Do the troops I moved in from another territory help defend the castle from the storming enemy? Or do my troops moved in from another territory first fight a battle outside the castle, and then there's a second battle against my troops inside the castle when he storms the castle?

if it's the latter, i suppose the only way to join forces is to order my troops inside the castle to break the siege? then they will join with the troops i move into the territory from elsewhere, right?