When connecting to my server, I will first get an error saying this mod is not multiplayer compatible. When connecting a second time, this error is not shown.

Ditto here. From the log file:

38.391 Error ClientMultiplayerManager.cpp:1074: mod-osm-lib-postprocess was registered for the following events when the map was saved but has not re-registered them as a result of loading: on_tick (ID 0)
38.392 Error ClientMultiplayerManager.cpp:99: MultiplayerManager failed: "" + multiplayer.script-event-mismatch + "
" + "
mod-osm-lib-postprocess"