As mentioned in the title above, the AI works absolutely fine, when the Multiplayer Warlords game is hosted on the PC you're using to play Arma 3 with.
However, as soon as you disable "Fast Travel" for everyone, including the AI and make it run on a Dedicated Server, the AI will seemingly just stop working, after having seized the first sector.
Apparently they will not get updated waypoints and instead they cycle on the SAD (Search & Destroy) order indefinitely.
Once you enable Fast Travel, everything will work as intended and they'll jump to the next spawn point, even on a Dedicated Server.
I have contacted BIS Support about it already and it was confirmed to be a bug, so I should wait for it to be fixed in the upcoming update(s).
Nonetheless I decided to open up a new Bug Report on here, so I can track the progress and check in on my ticket every once in a while, until this issue is finally resolved.
As I don't like to play Warlords with said option enabled, it is quite a game (mode) breaking issue for me and I hope it gets addressed at some point in time.
Thanks for all your hard work btw. I really appreciate it.