Earth's spin obviously causes planets to rise in the east and set in the west, just like all other astronomical bodies. However, when tracking their positions month after month at the same time of night, the reason for their movement is not so obvious.
If going by sidereal time (star time) the planets (excluding Mercury/Venus) actually move west to east because that's the direction of orbit (CCW when viewed from overhead.) Sidereal time is the actual time of Earth's spin. The difference between sidereal and 'regular' time is accounted for by the fact that the Sun and Earth move relative to each other (Earth's orbit) so the Earth has to make a full spin and then some to put the Sun back to the same point in the sky, because the Sun moved a bit, so it takes longer.
Going by 'regular' time (Sun time) straight up at midnight at a specific Earth longitude points to a different direction depending when in the year it is (30deg/month), unlike sidereal time. This very fact makes it confusing about how things move relative to each other, which is why astronomers use sidereal time rather than 'regular' time. Going by regular time gives the appearance that planets orbit CW rather than CCW (Mars and beyond don't orbit as fast as 30deg/month.)
