A timed extension of input-driven pushdown automata (also known as visibly pushdown automata and as nested word automata) under the event-clock model was introduced by Nguyen and Ogawa (“Event-clock visibly pushdown automata”, 2009), who showed that this model can be determinized using the method of region construction. This paper proposes a new, direct determinization procedure for these automata: an n-state nondeterministic automaton with k different clock constraints is transformed to a deterministic automaton with 2n2 states, 2n2+k stack symbols and the same clock constraints as in the original automaton. The construction is shown to be asymptotically optimal with respect to both the number of states and the number of stack symbols.