Alright, I'm running the game with Exerelin, Neutrino Corp, Shaderlib and Lazylib.
First of all, Neutrino Corp does not add any new potraits. When you select the campaign, it should ask you "How many systems", "Max system size", "Max planets per system", "Max asteroid belts per system", "Max stations per system", "Is the omnifactory available?", "How many other factions in Exerelin initially", "Shall factions return to Sector Exerelin?"
Then as final question it will ask what faction you'd like to join. It should give you these choices:
-Start unaligned
-Hegemony
-Tri-Tachyon Corp
-Sindrian Diktat
-Neutrino Corp
Then it will ask: "How populated is Exerelin", and if you pick the Neutrino Corp it finally gives you a choice between a few Neutrino ships:
-Relativity-class Drone Frigate
-Singularity-class Balanced Drone Frigate
Did it give you these choices?
If you're not running it with Neutrino Corp it should do all the above, except you'll only be able to pick vanilla Starstector factions.
Also (I think this is what has you confused), Exerelin no longer allows you to capture a station upon startup. Your faction will start with its own station and it should say in which system at the start of the game. Those videos you saw were probably of an older version of the Exerelin mod. In the latest version you just start with one ship. But you can capture stations later one when you've got troop transports and lots of marines.