I was ACRI... Directly did Brigade level training in Kenya, but also did some other stuff. At the time, there was no AFRICOM (I did do some work setting that up with MARFORAF, but that's a whole different story). Most of ACRI was through EUCOM, but Kenya was definitely in the CENTCOM AOR.
The whole idea behind ACRI was to train African forces in Humanitarian and Peacekeeping options. US SOF was usually responsible for training as they own the FID mission, but there are always exceptions... like when the Host Nation wants something else. DOS was responsible for funding and acquisition of equipment, and coordination with the HN, but were not directly involved in the actual training evolutions. From the funding perspective, remember Congress authorizes the funds and the department that has the authority to spend.
ACOTA was slightly, but not totally different.
Because ACRI was focused (and limited) by the peacekeeping mission, what we could teach (and the uses of the equipment provided) were limited. This was not necessarily a DOS restriction, it was written in the Congressional authorization, though DOS did like to play policeman on that. Neither ACRI nor ACOTA are meant to train HN to be solid COIN fighters, and to expect that as an outcome is to set things up for disappointment.
Now FLINTLOCK, on the other hand, has a completely different mission set. And I'm going to keep my opinions of that evolution cleanly off a public forum.