Clash on Kingsroad objectives question

By midwestborn86, in Battles of Westeros

Do objectives change sides in this battle? If I occupy a hex with a Lannister unit would I replace the objective marker with one of my own and would it not again change until Stark retakes it. Or are the victory conditions simply implying Lannister must have a unit in each of these hexes at the end of the fifth round to win?