I will play the Devil's Advocate on this question. "The question How to figure out someone is plagiarizing the future? is not about building something, shaking out the rules, or even exploring the consequences. It’s about plot and there is no way around it." As a good Devil's Advocate I shall be taking the contrary case and defend it against the charge of being plot-based.
I will observe that plot is something much more complicated and subtle then seems to be its usage on this site. TL:DR the question is not about plot. Any answer explaining plot would be longer than is reasonable for an answer here. So I leave it with the observation this question isn't plot.
What it is about is exploring the consequences. Specifically, about the consequences of someone stealing intellectual property from the future. More specifically, about the consequences of that theft that lead to its discovery.
Now, the question itself, isn't exactly well framed and doesn't seem to have been thought through as cogently as it might have been. Sorry, to the OP, if you see this, but thems my opinion. By that, I mean my professional opinion both as a published author and as a former paralegal adviser; note that this is just what I think and my opinion is as good as anyone else's. The clunkiness doesn't make it easy reading. The fog of imprecise words and phrases can lead anyone to think this is all about plot. It is a worldbuilding element which will, presumably, go towards shaping the plot of the OP's story (if that is what the OP is doing), but it still is a worldbuilding element.
Possibly, this question could have been better framed along the following lines. I am sure others will be able to construct better versions of their own. If someone was stealing information, knowledge, science and technology from the future, what consequences of this scheme will lead to its discovery?
I quote the following statement by Monica Cellio:
The scope for Writers includes the following relevant explanation:
Asking to brainstorm ideas tailor-made for your particular story is
off-topic; that’s too specific to your own work. But identifying a
general scenario which naturally presents plotting difficulties is
Those same reasons apply here.
These words appear in Storytelling and plot building
The question under discussion here is an example of a scenario with plotting difficulties and by exploring its consequences makes it on-topic.