What do the arrows depict in the optical-flow visualizations such as the one below?
(image source: learnopencv)
Is it correct to say that the pixel at the tip of an arrow was at the origin of the arrow in previous frame?
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Yes, as your linked page shows:
the idea is that the pixels move from $(x,y)$ in the first from to $(x+\Delta x, y + \Delta y)$ in the second. I believe the image you quote is just connecting a series of $(x_i,y_i)$ with their next locations $(x_i+\Delta x_i, y_i + \Delta y_i).$