The workaround to this bug, i.e. a culture victory not triggering despite meeting the requirements, is this:
- Load a game from a couple of turns before gaining more foreign visitors than any other civ has domestic tourists in their own cities.
- Continue playing the game without saving.
That's it. What messes it up is the act of saving the game on the turn before achieving cultural victory. And yes, you need a saved game (autosave will work, but if you miss it and autosaves don't go back far enough, you're out of luck) to be able to do this.
Almost 5 years on from a couple of Deity victories and I've finally had another go at playing. I wanted to go for some new achievements this time, and one was that I still hadn't won a culture victory. So, believe it or not, I ran into the same bug again. I'd been half-expecting that, so had saved pretty much every turn leading up to it (which, ironically, ended up causing the bug to manifest itself).
The next closest civ (also Kongo, for the "Selfie" achievement", hence it shows up twice in the screenshot) had 54 domestic tourists, so I needed 55 foreign tourists for a culture victory. I checked every few turns as numbers were creeping up quite quickly, and suddenly I had 58/55, but no culture victory.
A bit of googling showed various theories, one being that you had to hit the number straight on, so in my case get exactly 55/55, to get the victory. I disproved that by going back about 2-3 turns and gifting a bunch of my great works to rival civs so I'd produce less tourism output. I hit the requirement exactly and still didn't get the victory. Another theory was that sometimes you had to continue playing a few turns - that didn't work for me (but someone insisted it had worked for them, so... maybe they stopped saving and played on to trigger it, can't say for sure).
This Reddit comment put me on the right track. I went back 3 turns, made sure I had fewer tourists than required, and just did nothing for 3 turns, not moving my units and selecting random techs or things to build. Sure enough, the game awarded me a culture victory and the desired achievements.
Hitting the "Just One More Turn..." and checking the culture leaderboard showed that I had again overshot the requirement, but by not saving the game for a turn or two, it didn't glitch out.
I'm pretty convinced this is a bug, but maybe it could be some misguided attempt at stopping people from sharing a save game just before a victory. It's quite disappointing that this bug has been around for such a long time without getting fixed or officially clarified as a "don't save requirement".
I'll leave the original post by toryan as the accepted answer, but I hope this explanation helps others who encounter this particular bug.