In the above image, the green line represents the potential southern reach of the northern lights the evening of April 10 into the morning of April 11. However, a representative from the SWPC notes there's no guarantee you'll see the spectacle if you're inside the range. "You need very clear skies, a good view of the northern horizon (no trees, buildings, or hills), and it needs to be dark," they said via email.
It may be visible, but this far south it's not likely to contain the brilliant ribbons you often see in videos when it's at its most spectacular. To see the Lights at their best you should head somewhere like Alaska, Iceland, Norway, or Finland.
Nonetheless, a solar storm like this provides an opportunity to catch the northern lights, which are expected to appear less frequently at southern latitudes over the coming years when the sun is at or close to the solar minimum.
If you're going to go for it, you'll want to be out around midnight or potentially even a little later based on the SWPC's 30-Minute Aurora Forecast. For the best view, get far from city lights, so you're looking at dark skies. The moon on the evening of April 10 will be waning crescent and won't provide much interference.
If you can't make it out Tuesday night, then it's worth bookmarking tools that could help you keep tabs on when the aurora will be visible in your area. The SWPC's 30-minute forecast and Aurorasaurus, which crowdsources aurora sightings, are both great tools.