You seem to be assuming that a decision making procedure should compute what action an agent should take to best achieve some goals. Under this assumption, it seems very important that an agent's actions can't affect the past. But the innovation of TDT is that a decision making procedure should compute what decision the abstract (not just any particular physical implementation) decision making procedure itself should output to best achieve some goals. Because the abstract decision making procedure is not a physical thing in space-time, it is not subject to the same limitations as the physical agent. The abstract decision making procedure really does control whatever physically instantiates it at any time (and indirectly influences whatever interacts with those instantiations).