I doubt Zheng made it to America, however. The voyages into the Indian Ocean are well documented, but there is nothing about sailing east across the Pacific. The maps are easily explained because the Chinese were well informed about the outlines of Asia and knew the geographical relationship between Asia and Europe across the Silk Road.
What Columbus did not know was how far Europe was from Asia going west from Europe. Had Zheng cirumnavigated the globe, the Chinese would have known that.
The size of the Earth was computed to reasonable accuracy around 250BC by Eratosthenes. That should have given him some kind of clue.