Yea, not sure about the whole tutorial situation.
But negative income doesn't really matter for anything other than it makes your bank account decline over time. In GC2 there was definitely a mechanic where deficit spending eventually had an impact on morale - but I don't think it exists at all in GC3 - although I'm not 100% sure on this, it's not something that's big enough of a deal that it's seemed to impact any game that I've played.
If you deficit spend so that your bank account falls below 0, then it cripples your production, yes. But otherwise spending more than you're making doesn't really matter.
As far as the production modifiers go, morale is actually important (if you mouse over your raw production numbers on a planet it'll usually list a morale bonus/penalty as a modifier to this), so it usually actually makes sense to try to keep morale high to get the better production by keeping a low tax rate, and just losing some money every turn because of it.
I'd try another game (again I'm not sure what's in the tutorial, but a sandbox game in a small galaxy with easy settings would be fine too) and not worry about the income/turn issue, because it's honestly not an issue until your bank account goes below 0. Limit yourself to rushing no more than 2 or 3 things, and you should have ample money to get a whole lot of turns under your belt and then I suspect that you'll feel a lot more comfortable with the various systems in the game.
There's definitely a lot of mistakes one can make in getting an empire off the ground, but honestly there isn't really anything in the game that warrants feeling bad about, and the game is never over until some alien conquers all of your planets - so the money situation or what you built when and where on whatever planet or whatever all just ends up being water under the bridge.
Best of luck!
edit: Oh, I should add - "building stuff" doesn't have much to do with money unless you "rush" it (ie buy it immediately, which costs money) or build something which has a maintenance cost (which usually costs 1bc/turn or whatever). Otherwise if you build something and it takes 8 turns, or whatever, after the 8 turns it's built and it didn't cost you any money to do that. So your money situation shouldn't impact your building or ability to build stuff really at all, except that you can't rush things, and if your bank account balance goes negative it'll reduce your ability to build/research by a very large %.
edit 2: FWIW the tutorial doesn't tend to get much love, so stuff might possibly be jacked up in it or something? Like I said, I've never played it, so not sure. I recommend just doing a sandbox easy game in a smaller sized galaxy and just fiddle around with it and see how it goes.