Replication:
Its taking me too long to build custom addons for you, but you should be able to replicate with your own modules.
!! The issue described is best visible on a freshly started local dedicated server !!
Ensure you have several modules with different functionPriority values in your mission.sqm.
Ensure some modules run clientside (isGlobal 1/2) and serverside.
Ensure init takes longer than 25-30 seconds overall
Startup local dedi instance, connect a local client to it
Login as admin and and start your mission (ofc. with several different modules based upon BIS module framework in it).