Greetings @TheMuslimWitch,
That’s a really great question! To the best of my knowledge, the modern Wheel of the Year was developed in the Northern Hemisphere largely influenced by Celtic traditions, hence why the Northern version of the Wheel of the Year is the one more commonly seen.
The Wheel of the Year is a symbol of the eight Sabbats (religious festivals) of Neo-Paganism and the Wicca movement which includes four solar festivals (Winter Solstice, Spring Equinox, Summer Solstice, Fall Equinox) and four seasonal festivals (celebrating or marking a significant seasonal change). Contrary to modern-day Wiccan claims, there is no evidence of an ancient Wheel of the Year in its present form but it is clear that the Celts of thousands of years ago celebrated the festivals the wheel highlights, even if these celebrations were known by another name now long lost.
In the ancient Celtic culture, as in many of the past, time was seen as cyclical. The seasons changed, people died, but nothing was ever finally lost because everything returned again – in one way or another – in a repeating natural cycle.
From World History: Wheel of the Year
I’ve seen that those in the Southern Hemisphere tend to follow the Southern calendar (as shown in the picture you shared), which follows the same cycle and holidays as the Northern calender, just adapted to suit the opposite seasons that the Southern half of the world experiences 
The Sabbats are inherently tied to the seasons and based around the qualities of that time of year, so it makes sense that witches around the world would follow and practice the holidays as they happen in the environment around them.
Although it is certainly doable, and perhaps there are Southern Hemisphere witches who follow the Northern cycle, I personally think it would be a bit strange to celebrate, for example, the harvest festivals of Lammas and Mabon when the winter is in full swing and the new life of spring is still a ways away 
However, many witches may live in places that don’t have 4 distinct seasons and/or live close to the equator- in that case, I’d imagine it boils down to following whichever system they feel attached to.
Disclaimer that I’m located in the Northern Hemipshere, so these are just my opinions and observations! Hoping to hear from some folks who live in the Southern Hemipshere to share their personal thoughts and experiences 
Blessed be to witches around the world! 