The Mars rovers, including Perserverance, usually communicate directly over a high-speed link with one of several relay satellites orbiting Mars. The smaller antennas of the DSN can communicate with the relay satellites as well.
Furthermore, the locations of the stations aren't determined by the hemispheres. Everything DSN is used for is far enough away from Earth that it doesn't matter if the antenna is in the northern or southern hemisphere. The reason for the spread-out stations is the rotation of the Earth, which for half of the day puts the Earth in between the station and the satellite.
While the rotation of the earth is one of the primary reasons for the spacing, the hemisphere does matter for Voyager. From the article: "As Voyager 2 is heading southwards compared to Earth's orbital plane, only a dish south of the equator can send the probe a sufficiently powerful signal."
Not necessarily, Voyager 2 is pretty far angled below the ecliptic plane by 48 degrees [1]. If you were to point the Goldstone dish (35 degree N latitude) directly at the horizon you can reach as far as ~78 degrees below the ecliptic plane if you are pointing in the direction of the tilt of the earth (I don't actually know where Voyager is relative to the tilt of the Earth). If it were in the opposite direction, pointing the antenna at the horizon means you could only point at something ~32 degrees below the ecliptic. And Madrid has a slightly higher latitude at 40 deg N.
Furthermore, the locations of the stations aren't determined by the hemispheres. Everything DSN is used for is far enough away from Earth that it doesn't matter if the antenna is in the northern or southern hemisphere. The reason for the spread-out stations is the rotation of the Earth, which for half of the day puts the Earth in between the station and the satellite.