I am not aware of any "overriding order" per se.
It could be that individual controllers work but two of them together conflict. One trying to increase fan speeds and the other trying to decrease fan speeds.
May be in conflict simply because of different temperature measurements and/or their respective + or - temperature accuracy.
Testing needed.
Look in Task Manager to determine if any fan controllers are being launched at startup.
Resource Monitor and Process Explorer (Microsoft, free) may also help.
https://learn.microsoft.com/en-us/sysinternals/downloads/process-explorer
Task Scheduler may reveal some related fan control app being triggered per some system related event.
I think the safest way is to identify all of the various controller apps and disable all but one of them.
Determine if the running controller is able to maintain temperatures, fan speeds, and steady performance overall. If so, then disable the first tested controller app and try the second controller app. Again to determine if the second controller also works as required.
So forth and so on.....
You will need to work out a test plan in advance to ensure that 1) that you never disable all of the fans, and 2) that you only change one thing at a time.
Keep notes: configuration, fan speeds, temperatures, and so forth.
Narrow down to which controller maintains temperatures and fan speeds reliably and consistently. Then use that controller.
Just my thoughts on the matter.