The equator isn't the dividing line, but the sun/moon are swapping exclusives. If you know the regions for Seviper + Zangoose; these use the same regions.
Currently...
North America, South America, Africa : Lunatone
Europe, Asia, Australia : Solrock
They last changed places around the Summer Solstice (late June 2018). Before that, their positions were swapped.
"Why didn't I see one until now?"
Recently, they changed various spawn mechanics so rare things aren't quite as rare as they used to be. Previously, Lunatone was a real bitch to get. Like, very late-night-only sort of thing, and some people even posited that it might need ~3+ solid hours of partly-cloudy weather before it would spawn. Since the change, they seem to have extended its hours (recently, I've seen it as early as ~8PM, and as late as ~10AM. Is it still time-gated at all? I don't know.) and/or just made it less rare. Weather also doesn't seem to be as important as it used to be. I've seen four Lunatones in the past two weeks, whereas prior to that, I only saw two Lunatones from July~November.
"Will they change places again for the Winter Solstice (Dec 21)?"
Maybe ¯\_(ツ)_/¯