Interesting question!
Not sure of the exact details in this case, but remember that they show 24 frames in a second. The duration that the frame is actually visible is shorter. Persistence of vision makes it appear continuous to the viewer.
The projector moves the film so that a new frame is front of the projector light 24 times a second. The projector light then actually illuminates the screen through that film frame for only some of that time (so you don’t see the film when it moves).
Apparently in modern projectors they still show 24 frames, but they show each frame (shine the light through the frame) more than once per frame.
As far as I can read the exposure duration is partially adjustable, but that 3000th of a second seems very short - maybe they added the subliminal projected images via a separate mechanism than the main projector – specifically to test short durations. It would depend on the detail of their experimental projector setup.
Does anybody have a reference to the original paper?