In the first it is correct to say 'he cursed as she slammed the door'. Two actions both in the past.
In the second we say 'Who was the one that made him cry'. Again we have two verbs in the past (was\made). 'Cry' is not in the past because it is an infinitive without 'to' and never changes:
She makes me cry (present)
She made me cry (past)