They're going from the south, because the south is mainly flatland, and easier to take, while the central regions under Armenian control are mainly mountainous.
Once the South is completely taken, they'll move towards the north, and start slowly taking the mountain ranges.
Taking the south first also serves to cut off Armenian troops in occupied territory from directly receiving aid from Iran. This way, Iran now has to go to Armenia proper first, making the Iranian supply lines longer.
I have doubts that Azerbaijan will actually launch a major offensive from the north. I believe they'll move from the south to north, perhaps along the Armenian-Azerbaijani border, to completely surround the mountains, cut off all supply lines, and slowly move towards the center. Though, going along the border, also risks Azeri troops coming into the firing lines of Armenian troops in Armenia proper, which Azerbaijan can't heavily retaliate, nor properly defend against, due to fear of CSTO being invoked.
Mountain warfare will be a painful experience for the Azeris, it will be slow, and it will be 10 times more difficult than what they've so far faced. The Armenians are dug in, and have the advantage, one that air power won't help much on. The safest (but slowest) method would be to find a way to cut off Armenian supply lines to troops in the mountains, and siege them, until they have no choice but to surrender.