This engine was designed to power aeroplanes. Aeroengine design was in its infancy at the time, and there was much debate as to whether two-stroke or four-stroke engines were best. A two-stroke engine would (in theory) give twice the amount of power for the same weight, but in practice there were difficult problems to overcome.
Korwin & Rebikoff seem to have decided that a three-stroke engine would be a good compromise between two and four strokes. The upper auxiliary piston drew in a fresh charge through the automatic inlet valve B at the top of the cylinder, and at the appropriate point in the cycle transfered it to beneath the main (lower) piston. This allowed great overlap of induction and exhaust processes without the partial mixing of charge and exhaust that occurs in two-stroke engines.
The valve in the upper piston was exposed to the full heat and force of combustion, but this is no worse than the situation of an exhaust valve in a four-stroke engine; in fact rather better as hot exhaust gases did not flow over the upper side of the valve.
No picture of an actual engine has been found so far.
Source: Scientific American. Vol 67, Jan-Jun 1909. Sci Am Supplement 1730, Foreign Aeronautic Motors-III Feb 27 1909 p133