Acetic acid and acetate are connected by the dissociation equilibrium $(1)$:
$$\ce{CH3COOH + H2O <<=> H3O+ + CH3COO-}\tag{1}$$
So you basically have two acidic particles that can react with hydroxide: hydronium or acetic acid. Hydronium will actually react much faster on a molecular level even though its concentration is significantly lower as it is much more mobile in solution. However, any hydronium consumed is immediately reformed by acetic acid molecules reestablishing the equilibrium.
Therefore, on a very minute level hydroxide reacts with neither acetic acid nor acetate but with hydronium which is produced in the dissociation of acetic acid. In practice, that still means that hydroxide will be added until $n(\ce{CH3COOH})+n(\ce{CH3COO-})=n(\ce{OH-})$. From this point onwards, there will be more hydroxide than acidic particles causing the $\mathrm{pH}$ value to rise significantly, the indicator to change colour and the student to realise that they reached (and passed) the equivalence point.