Let's put that idea to proof.
The odds of getting at least one drop are dependent on how likely you are to get a drop and how many times you roll the dice; P(drop) = 1-((1-p)^n), where p = percentage of getting a drop and n = how many times you've rolled the dice. In other words, better odds of getting a drop are dependent on how quickly you can get n to rise. If you're doing every CE and FATE in South Horn as it comes without concern for what Demiatma can drop yes, it's more efficient because FATEs and CEs spawn at about the same rate as FATEs in the overworld and you'll get to enjoy the higher drop rate from CEs (though they do tend to take longer so... even shake?). The formula for that looks a bit more complex, but basically you just calculate (1-p)^n twice using the different statistics for FATEs and CEs and multiply them before subtracting them from 1. However if you're gunning for a specific color because you're almost done, focusing on overworld FATEs will raise n faster than waiting for the right ones or CEs in South Horn. In half an hour you can do say 20 overworld FATEs (assuming a 5% drop rate, 64% chance of getting a drop) or 10 South Horn FATEs and maybe 2 CEs (respective 5% / 20% drop rate gives you 14%) gunning for a specific color.
I'm just guessing how many FATEs and CEs you can do in that time frame, but the n for a given color will rise faster outside of South Horn for sure so... whether it's faster to grind in South Horn or an overworld map is dependent on whether you're going for any Demiatma drop or a specific color, assuming FATE drop rates are equal in South Horn and that color's dedicated overworld map. (Might not be.)
(Note: P(drop) will never reach 1 a.k.a. 100%, so if you're supremely unlucky you still will not get any Demiatma no matter how many times you roll the dice or how high the drop rate is, assuming the pity system in most modern virtual gacha systems is absent as it seems to be here. Statistics, gotta love 'em.)
EDIT: Spent an hour grinding Yak T'el and Living Memory, got one (green) in 25 FATEs. That's a 4% drop rate, about on par with the reported 5%.