We address the problem of alternating simulation refinement for concurrent timed games (TG). We show that checking timed alternating simulation between TG is EXPTIME-complete, and provide a logical characterization of this preorder in terms of a meaningful fragment of a new logic, TAMTL∗. TAMTL∗ is an action-based timed extension of standard alternating-time temporal logic ATL∗, which allows to quantify on strategies where the designated player is not responsible for blocking time. While for full TAMTL∗, model-checking TG is undecidable, we show that for its fragment TAMTL, corresponding to the timed version of ATL, the problem is instead in EXPTIME.