Ok I just found a thread with some conceptual explanation of PtA having effect in the present, though not the math. But this does clarify something about (his thoughts on) the effect of the future on the present.
Einstein even went so far as to observe that since all of time can be captured in a mathematical equation, there is no reason for it not to progress in both directions. Even though generally agreeing that the future is influencing the present, James had issues with Einsteins model, as expressed in these threads below. He did not accept that there is no objectively true situation. A lot of ILPs smartest posters have been wrestling with him on this, I wonder if you can solve it. I lean toward the the critics position these days, that it is simply not the case that we can calculate across/between reference frames, but I am still not sure.
But back to the topic; in James’ definition of particles, an atom largely consists of what it will do in the future. Which is logically quite true. We can also say that the future consists of all paticles’ combined PtA, but that comes down to the same. Key in both AO and Relativity is that objects/entities are not three- but four-dimensional. My own ontology adds a fifth dimension.