Yes its the same time down here too. Ignoring for a minute the difference between the Tropical and Sidereal Zodiac, and also what is actually happening in the sky, which neither represents...
Aries starts when the Sun moves into the area of the sky attributed to Aries (by whatever method you prefer). So it doesn't much matter where on earth you are, its still a straight line from you to the sun and onwards to the appropriate section in space. The only difference is is it day time or night time. Cause the line that starts with you might go directly out into space, or it might have to pass through the earth and out the otherside on the way to the sun.
But doesn't matter which hemisphere your in. We even have the same moon phase happening down here as up there. Though recently I wonder if we don't see the moon from a different angle. Haven't got around to thinking through the maths of that yet, but artistic representation of the moon always show it waxing from the right hand side, but my local moon seems to wax from the upper left.... hmmm...