Zheng sailed west and definitely was in Arab world and E Africa, but no evidence he ever entered the Atlantic or Mediterranean. Or sailed East, across Pacific to America.
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.