I confirmed this behavior on my end and created case CPANEL-43323 with our developers so they can look into this. I'll be sure to post any updates I get!
I did reach out to the team today, and they are aware of the issue but work hasn't started just yet. It would seem that the Tweak Settings values only apply to actions inside the File Manager, so there is definitely work to be done to clarify things in this area.
I they provide me with this command that will help check the I/O nice value of the doveadm processes, so this could be worthwhile to check on your system as you likely won't get accurate data directly from "top"