How tightly do the various parts fit together?
I think it might be a self-regulating system (which Premiers are up to a point), where the pressure of the generated gas keeps the water "at bay" until the pressure drops a little, allowing a bit more water in, to generate more gas, and "push back" the water so it won't flood the inner chamber. If you draw a section through the assembled lamp, it may provide a clue. How well the different bits fit together might confirm this idea, or kill it.
So, as I have sketched it, water in the outermost part, makes its way between the different concentric cylinders into the innermost chamber where the carbide is. The gas escapes up the "chimney" to the burning nozzle.