Hilchos Maasei Hakarbanos 7:11

Everyone who ascends the altar on the right goes around it and descends on the left except for someone who goes up to do one of the three things that are done on the upper half of this corner. Such people go up on the left, turn left to that corner, perform their task and then go back the way they came. The reason they turn left is so they won’t come to the southwest corner first. If they were to turn right and go around the whole altar until they reached the southwest corner, the water or wine might get tainted by smoke from the altar, or the bird for the offering might die from the smoke.

Hilchos Maasei Hakarbanos 7:12

Pursuant to the previous halacha, if a kohein who is to perform a water or wine libation circles the altar, he must do so emptyhanded. He starts at the southeast corner, proceeds to the northeast, the northwest, and finally the southwest, emptyhanded. When he reaches the southwest, he is given the water or wine to perform the libation. If he doesn’t want to go around the altar, he may go up the ramp, turn left, perform his task and go back down.