please hold the applause.
No, because you're right - this is a serious bug which is totally gamebreaking on tiny and small maps.
I couldn't find anything helpful explaining the tourism-income so I made a few tests in order to compare numbers:
Using Torians @ 0% influence from turn 2:
Dreadlords:
Tiny galaxy: Taxes: 34 bcs Tourism: 3 bcs
Giga galaxy: Taxes: 34 bcs Tourism: 0 bcs
Dark Avatar:
Tiny galaxy: Taxes: 23 bcs Tourism: 4 bcs
Giga galaxy: Taxes: 23 bcs Tourism: 0 bcs
Twilight:
Tiny galaxy: Taxes: 26 bcs Tourism: 153 bcs (!)
Giga galaxy: Taxes: 26 bcs Tourism: 4 bcs
So it seems like Twilight did incorporate some changes to increase the Tourism income (which actually is a nice idea to counter the initial going broke after the colonial rush). On Gigantic it seems reasonable, but on Tiny it is totally out of whack. Using SuperDiplo with all points put into Influence I am able to scoop up to 275 bcs (!!!) from Tourism alone in turn 2. That totally defeats all purposes to establish an economy.
But it doesn't have anything to do with the new .EXE (haven't got them right now) this bug also appears in the unmodded game.
After reinstalling the game, with CU enabled and the new exe copied into the Twilight directory, the economy seems normal. Something got corrupted! Gremlins in my computer!
Actually I've encountered this bug before when working on my personal mod but I couldn't isolate the source of the problem. I noticed it when I worked on some raceconfigxml or the raceconfig but reverting bakc my changes didn't stop this bug. The only solution seemed to be to reinstall the game, deleting all folders manually after deinstallation then it was gone. But when I implemented my mod again the bug reappeared, so I gave up -.-
What befuddled me was that this isn't calculated until turn 2
Actually Influence is always calculated like this. When you, for example, reload a game you'll notice that your zone-of-influence borders are slightly diminished - expanding a turn puts them back to normal. The only way to make them normal in turn 1 is to build something that triggers an influence-recalculation, such as colonizing a planet or building a starbase.
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I've made some more tests and I think I could isolate the bug to the starting planet. First of all, the sphere-of-influence it creates seems to be pretty heavy, it encompasses nearly 100% of a tiny galaxy if there wouldn't be another player present.
Colonizing the second planet, and relocating the inhabitant from Toria to the second initial colony. Afterwards, I've destroyed Toria and got this pic:

Stats are:
Torian Influence: 70% vs Krynn: 45%
Torian Population: 8b vs Krynn: 8,7b
Torian have 1 Influence Starbase. (build as the very last thing in order to trigger the influence recalculation)
Actually their zone-of-influence should be equal, or probably in favour of the Torians.
But the Krynn still have their original homeworld while the Torians are on their secondary planet (its Initial Colony building got automatically upgraded to a Civ Cap)
TBH that seems to be quite gamebreaking. Investing into Influence on Tiny/Small maps seems to get a better economical return than investing into economy (!) and it also brings other bonuses such as culture victory, flipping planets and IPs.