Hey Lochar,
First let me thank you for being the guinea pig on this and thanks for taking the time to post the feedback! The early game balance is still pretty rough, for a number of unrelated reasons including user feedback. I can usually get through it myself, but I'm kind of at an advantage here for obvious reasons.
It's hard to say reading your post what exactly what went wrong but let me outline some steps so we can get to the bottom of it. I will be duplicating information you might already know, just want to be complete!
So first thing to do is assign someone to the starting reactor. You're looking for a crewmember with a Physics skill because the reactor jobs all use that. You can get to the character sheets from the Crew app and see who has what skills. Likewise if you click on the reactor section an info panel should pop up, and somewhere in there it should tell you the job uses Physics.
Something else that's going on behind the scenes is that when a worker executes his tasks it matches each task against one of the aspects of his personality. This represents people being naturally inclined to like their work or not. If a crewmember starts the game with the Physics skill then he already has the associated personality aspect within his starting trait (he has the Physics skill because his personality has the aspect that makes him interested). If nobody has a Physics skill, then you could look at the personality traits of the crew and find someone whose personality sounds like he might do a good job. We've planned another pass on the trait definitions which should make this more clear, but for now give it your best shot. Just don't pick someone that sounds like they have a negative personality and you should be alright.
Second thing to consider is that Physics uses the Mind stat, so to execute tasks the reactor operator will be using M. So another thing you could do is pick someone with a high Mind. Sleeping regenerates BMS, and if he's squatting somewhere then he won't get a good night's sleep. Conversations can add or subtract to BMS -- this is like you get in an argument and it totally drains you, or you see a friend and he gives you some encouragement and boosts your energy. So if your reactor operator gets in spats with some other crew (you can check his conversations) you might stick the person your reactor operator is fighting with on the shuttle and send the hated person off to do missions to keep the two separated. (On a larger station you could assign them to be far apart from each other). Just so they aren't constantly exhausting each other with arguing.
Next thing is if you click on the info panel for the reactor section again, it should tell you the resource that the given reactor consumes. If the resource is a liquid then it will get refueled via a conduit (the conduit will just move the liquid from the cargo hold, since that is what conduits do). If there is no conduit, then some custodian will need to do the refueling manually so you'll want to build a custodial facilities in this case, and also assign someone to the cargo hold to pack and transport the resource to the reactor.
Let me know if that helps!