Cumulative and does carry across multiple missions.
As the tutorial is very brief, I didn't really pick up the terminology. Modules are what you build on the space station. Systems are the wiring elements you link up in the ASL.
As far as I can tell, everything counts towards this; orange or blue slots and any of the module categories.
This should unlock before you complete all of the missions, so there should be no need to go out of your way to get it.
Good luck!