This sounds like walking into a classic heffalump trap. Whenever Buddha was asked a question about the soul, he would say first, exactly what do you mean by soul. You should ask, exactly what do we mean by cause - eg arguably it is a narrative heuristic not fundamental now in science Is the idea of a causal chain physical (or even scientific)? Then ask exactly what was Buddha talking about that is interpreted now as causality.
Causality, karma, in Buddhism, is essentially psychological, narrative. And the SE post in link above shows how that makes sense in terms of modern thought. In Buddhist thought suffering, clinging, begins when there is conceptualising, abstracting - ie where ignorance and delusion become possible. The chain of dependent origination narrates arising from that. In the conventional sense, these are causal, preceding effects. They happen in loops though.
The conundrum for Western thought about 'who' makes the decision to raise a hand if it is shown by experiment to have already been made, isn't an issue for Buddhism. Which always viewed consciousness as the result of aggregates, heaps, arising at the gates between internal and external realms. In modern thought we have the workspace theory of consciousness, in which a range of unconscious processes compete for our awareness, and when they enter it they can be integrated into the self-conceptualising narrative - the strange-loop quality subjectivity and complex consciousness are deeply tied.
"Intention (cetana) I tell you, is kamma. Intending, one does kamma by way of body, speech, & intellect." - The Nibbedhika Sutta, Anguttara Nikaya 6.63.
I understand this as how there are all these threads and chains of karma, of narrative or dependent origination, and when we bring them into our awareness our workspace, we impart the qualities of our intention to them, our own personal karma. The consequences continue outside of that time, that awareness, when we make our own karma with the infusion of our awareness. Buddha had to face the consequences of his own karma from before awakening even after his cessation of creating karma, the consequences of what he had clung to in the past would have to exhaust themselves, even after he attained unshakeable liberation from clinging.
I hope this helps. I'm not sure I've really answered your question, because I am pretty sceptical about what you have presented.
Edited to add:
I shoukd be clear that my perspective is Mahayana yogacara school. Just been reminded of Vadubhandu's 20 Verses, and reading
"Vasubandhu's Viṃśatikā (Twenty Verses) repeatedly emphasizes in a variety of ways that karma is intersubjective and that the course of each and every stream of consciousness (vijñāna-santāna, i.e., the changing individual) is profoundly influenced by its relations with other consciousness streams" - Dan Lusthaus
Also a clearer description using canonical language of what I was trying to say about 'infusing':
"[T]he Sautrantikas [...] insisted that each act exists only in the present instant and perishes immediately. To explain causation, they taught that with each karmic act a "perfuming" occurs which, though not a dharma or existent factor itself, leaves a residual impression in the succeeding series of mental instants, causing it to undergo a process of subtle evolution eventually leading to the act’s result. Good and bad deeds performed are thus said to leave "seeds" or traces of disposition that will come to fruition." - Dennis Hirota, from here
It should be said there is another fundamental source of discontinuity between Buddhist and Western thought. Buddhist philosophy is meant to be used, 'realised', through personal practice. It cannot be seen purely a book-keeping of account of mechanics. For Western thinking, the defining context thinking is orientated around is experiment. For Buddhist thought it is experience, and that is the ground it is built on because that is it's concern, that is what it is for.
