If I am in Philadelphia I am in the east and see the sun rise in the east (or the planet venus for instance). I get on the freeway or toll road and head east, and the sun seems to follow me, or if I take a rest stop, by late afternoon as I near Chicago (in the west) I seem to be following the sun, as I travel east to west. If my journey takes several weeks, rather than one day, then the planet which rose in the east as I began my journey may appear each night in the sky and seem to keep pace with my journey, depending on its orbit.
of course we know the celestial body is not rising, rather my vantage point for viewing is changing due to the earth’s movement, and to a lesser extent my own movement on its surface.
there is no problem or conflict in the biblical accounts about the star or the magi that has anything to do with use of the word East.