I am 14 turns into a new game and I have already discovered 4 minor civilizations in my home sector (first screen snapshot below).
I don't know if it will be useful, but I have included a link to a save file showing this:
https://www.dropbox.com/s/wwoav91zhpr6c7q/Minor%20Civilizations%20Under%201.50.374094.GC4Sav?dl=0
The second screen snapshot below shows the settings for the game and shows that I set Minor Civilizations to Occasional (by the way, thank you for not resetting everything to Default and retaining my previous settings when starting a new game).

