You route in the direction opposite the grain so the cutter isn't cutting into the grain. To make that clearer, you look at the corner you're routing. Assuming the post is vertical, you will notice that the grain is not straight down the length of the post. If the grain is slightly diagonal, going toward the top, you will start from near the bottom. This will avoid chip outs that would often happen if you started from the top with the cutter gouging into the grain. You'd have to check all four corners because that grain pattern would be reversed on the other side or opposite corners.
If you're using a trim router for this purpose, I'd not make it more than a quarter inch round over, with a bottom mounted guide bearing. I'd let the bit cool down a little before starting another side. With a quarter inch shank, the bit is more vulnerable to coming loose and flying off, so I'd stop every few passes to check the collet for both tightness and make sure the bit isn't bottomed in the collet, but about 1/8th inch from th
the bottom. You don't want to be anywhere near that thing if it comes loose.